rv

TJ1l9llU n 9119

~ r 22 7 2001 - N TUlTI

(0 t ~N OlED nlnilllJ ilPnJ

Jgt 0 (TIlED npJlpoundIpn7 N1Jn)

yen ~O nUDil mlNtDil U]lND OJl1W ID ilm

D1~ II lJ1nW nln~Wl 91] wnnWill DNWl IPrnlnil ~m DnJJW - mrn

nlNJil nPJJnil npml 1 iliNUJ

III III mJJnJ (nn~ruln nlls] mmj1J) mzm nlJJnn nN mnNil Hopfield nWl nlJ]I W

111Jf

11JD nNf nlNlill jI9OD ) 1m n1JJnilW lNln1 IP1Wjil n~llln nN nwn N il~11J9Jljil IW ilnlNil nn iljinPiil Iw mJS m~11P9Jji mClnn nnN

mNTil

Nil mOlil OJ n~11l911jiil t=O lnTJW TIll J

liD) nnlTO iljiml] ilJ1JNillWl n~lU9J1jillw mfJ mnngnilil nN llNn (lllJji llJill

ill]jin iljiDP11nll ] 9llO I]) 11m 1

~[il ~2i mJllJT JW O])]JjlTI il]W OlP] frlll11 N Iw nJ1Dn iUlm 2 ni~ID p == a lJOJ ~ Ii -= 1 m1WNlil nJJn] Hopfield I11n Iw IP1Wji n~llln nlD~mD

p = I - a 1JO] ~2i = 1 il)[Dil nlJn]l

09N nl1~19tJ~J1 T n91U illm19D~J mlnil IW D]~il DEnil m~ mm N

nlnnil EnD nJ1JJnn nn9nn ]~n ilPN7 ] i IJI Sj = 1

m~~mil ID a Iw ilJJ9Wilil ill]

n1NWl nNTil illjiOnn DNil 0 lt a lt 1 IJ llJD D]~ mlllJTil )W T = 0 J J

(IW1]I i1l1WN1il n)]nJ lTIJ Dln]] ~i n lWN ) WIW 111JT D9U11J TIN i1l1JJmiddot

TIlNJ1 TIlltP]ilJNl TIlllmuifN TIllDn 3

iPUrtJ1Nl (E) TIlll~HPUifN ilUlJ1ND TIJJllD UJ111J TIJ1DD U]lll) 7[[] (I) nlltPJilPN

nlUl7J1Nil nUJ 7UJ lJslDDn il Jsif 1m nPDP1il TIlN110J1Jn nN mUll eN 1mJ 0)111) ]UJ 7J rJ PJ9PUil UlOJjlillUJNJ INP7n 71mJ

nmJ iPsUifln J1JT WE1 1 ~s npUl7J1Nn pJ1 I Wll 1 WEB un nlUlJmil

HI 1 HE JJ1JjI JT~n rJ7j1 D1 [[] nrDltJ1Nil nOJI 71 1 7s un np01J1Nil U11lD19il J1JJ 11JD (J

Wll=O WEE =

Wm =-WEl =1

HJ =-HE =-10

nN llifn1 TIllJlsJtJil nnlifJi1 TIN INsl1 U1SDil Jnl111 TIlJtif1Jil nN 11s

(L) 7[[] ilsif119J lTI1JtJJ ill1lTil 11if nN1 r91N Cs

1DTil IUJ il~if)19J npmJmn nm 1[1] 111 Jsjl nN 1lDJtJ 19mJ 11~ (1

nUllJT p UD 11991i1 nun 4

nJ 191NJ lnJJ ~ IJ lillNJ ~ lllJT n1JJn P I1J1 17991n nun m1m

Pr(~ = plusmnl) = t lJUil 91 17n

UJ 1J UrJ9PtJil UlOJifil nN NlifN 191NJ DJTIln Pr(Jij(n2W) =Jij(od)) =a

Pr(Jij(new) = 0) = I-a

nm1il1UJNJ UJVlil DDl DsmD TIN1 qht 7UtJil 7illDsmDil nN lJOJn eN

1 11lJTJ nN~m

qgt TIJ1nmo nJJDil DlJifDil P ilUJ illD17 TIlN tJn nptJN nlTDJ lNlil (1

aNP =-- N1i1 il)~

mlt 2InN

i

i I I

I I

1( IT -+ 0 llJD) NJil J1TifJ lUJDn[[]il I I

l bull co rIbshy1

Pr(-b lt X lt co) = fe -

21 dr == 1- r--e ()-

2 ~27()2 -II I27 b

Nil u lUJ tl7liii j1 ~1N ill1) IUl V m1l9i1 UJ iliTTllTil 3 ilNUl

v =tanh 13u1

gt0 ltJDU 1391) iillj T tU (Tt991i1 HTIWT) uTm~ Ollm 0]111] )W

h l1~n rltV DtJiDl

iliW IPl1Wil DlJNil m~ 11JOill nJ1UTJil tW irJ11Nil nN lJ11J N

iP11JNil W JIlNnJil nlTJJ 1il7U9il nN ilJlDU JlJllJUililD ilPlT)JIiilrll lN1il J nTIJjllD

CpO-lN lN1W ~ID UD il1li ilTJ nlJOil l

Olj7Dil IJ1D1 V TIN iN~n V = = V oJ iJiinn illnmii-W DlDIJTJilW ilnJilJ 1 ONJil

T=O h=O bullbull 1

TgtO hgt1 2

JilNJil TI1NlHllTJil T ill nlN1TITJ O]111J nllU17J1N TIW ill TI1ill9il 4 il~ill

=x(3 - x - 2y)

y=y(2 -x -y)

TIrD1J1Nil TIm ill TI171119il J~i TIN up~m xygt 0 1WNJ

71 iltW nlJ~il ilTJl nJ1lJTJil 7W TIJWil TIlTij] lilTJ N

111 ilTJlTil llj1 TINl (xy) 11WDJ TIJ1lJDilW nullclines -il m~ ltJmw J

(DJI~Iil tP~Dn) J~il ~Dil tW ilJIWDillJN TIN nlJN 19m1 1Nn 1

~-~ =rjJ

~+qr=sx x-z1nlp m e

CLG~ tnt LUlXNL

C rt~L QliC LLCU4U~ i x CNlllL Traquo ItCllxl umCl NU (t)tC (t)X C1Qt~a dXLQ lun LINlL

C LINLL CNlGt (~ClLI~ NU dLL~ LL~QL ra~tnlL (tC x) N CXNL Nt Qmcrq tnt LQIILCU lCLcJ1 NU ~t~ClUQ

x (1- i + zx) tC --ZuePIB x-yJ

x (1- ztC + ox)x -ZtnnJIemiddot tC =q

L umCl NU lNrLC~ tnt LLnU CC~ tntc tnt lL~trML (QQG~ IiCU NUL qL~a)

UNLl NU UGUUlU ClQt CLitQ~c1L adct 5ClL f = Lf l f- = 1 bull

C rr~u tnL UXlt cJCLLt 1 lC1Ql 0 =l LcJltGClLX mt LtnU L~

C LNQ N~l ucr~lU LULlU L~li~CLUl

N LNl tnl Nd QIt

calLt lGGlLmiddot

WalCl NU QClLXU ldalLq NtnL UCGhU tnlllU ucr~lU LN4l X~ClU CClQGLCllL NOO l~tN lZlL U~liLr~

r 1) ruUlU LUCr~lU LCNlU

LCll- mIlUQ LUt lUtQLq LtnNQ tLlllUCUlI CLI LlllCllU mlct 1It ~LQ

atL 11 tntllll CNLCft LlllNtlU LCNlU

(CltCLN -tUcIllLC~LLI ~KC~LI) CU(L CLIllLILl ~KCrJJ NI

CLlL C - WOI6Z GLLG U ClClGLLtL

Nil u lUJ tl7liii j1 ~1N ill1) IUl V m1l9i1 UJ iliTTllTil 3 ilNUl

v =tanh 13u1

gt0 ltJDU 1391) iillj T tU (Tt991i1 HTIWT) uTm~ Ollm 0]111] )W

h l1~n rltV DtJiDl

iliW IPl1Wil DlJNil m~ 11JOill nJ1UTJil tW irJ11Nil nN lJ11J N

iP11JNil W JIlNnJil nlTJJ 1il7U9il nN ilJlDU JlJllJUililD ilPlT)JIiilrll lN1il J nTIJjllD

CpO-lN lN1W ~ID UD il1li ilTJ nlJOil l

Olj7Dil IJ1D1 V TIN iN~n V = = V oJ iJiinn illnmii-W DlDIJTJilW ilnJilJ 1 ONJil

T=O h=O bullbull 1

TgtO hgt1 2

JilNJil TI1NlHllTJil T ill nlN1TITJ O]111J nllU17J1N TIW ill TI1ill9il 4 il~ill

=x(3 - x - 2y)

y=y(2 -x -y)

TIrD1J1Nil TIm ill TI171119il J~i TIN up~m xygt 0 1WNJ

71 iltW nlJ~il ilTJl nJ1lJTJil 7W TIJWil TIlTij] lilTJ N

111 ilTJlTil llj1 TINl (xy) 11WDJ TIJ1lJDilW nullclines -il m~ ltJmw J

(DJI~Iil tP~Dn) J~il ~Dil tW ilJIWDillJN TIN nlJN 19m1 1Nn 1

~-~ =rjJ

~+qr=sx x-z1nlp m e

CLG~ tnt LUlXNL

C rt~L QliC LLCU4U~ i x CNlllL Traquo ItCllxl umCl NU (t)tC (t)X C1Qt~a dXLQ lun LINlL

C LINLL CNlGt (~ClLI~ NU dLL~ LL~QL ra~tnlL (tC x) N CXNL Nt Qmcrq tnt LQIILCU lCLcJ1 NU ~t~ClUQ

x (1- i + zx) tC --ZuePIB x-yJ

x (1- ztC + ox)x -ZtnnJIemiddot tC =q

L umCl NU lNrLC~ tnt LLnU CC~ tntc tnt lL~trML (QQG~ IiCU NUL qL~a)

UNLl NU UGUUlU ClQt CLitQ~c1L adct 5ClL f = Lf l f- = 1 bull

C rr~u tnL UXlt cJCLLt 1 lC1Ql 0 =l LcJltGClLX mt LtnU L~

C LNQ N~l ucr~lU LULlU L~li~CLUl

N LNl tnl Nd QIt

calLt lGGlLmiddot

WalCl NU QClLXU ldalLq NtnL UCGhU tnlllU ucr~lU LN4l X~ClU CClQGLCllL NOO l~tN lZlL U~liLr~

r 1) ruUlU LUCr~lU LCNlU

LCll- mIlUQ LUt lUtQLq LtnNQ tLlllUCUlI CLI LlllCllU mlct 1It ~LQ

atL 11 tntllll CNLCft LlllNtlU LCNlU

(CltCLN -tUcIllLC~LLI ~KC~LI) CU(L CLIllLILl ~KCrJJ NI

CLlL C - WOI6Z GLLG U ClClGLLtL

~-~ =rjJ

~+qr=sx x-z1nlp m e

CLG~ tnt LUlXNL

C rt~L QliC LLCU4U~ i x CNlllL Traquo ItCllxl umCl NU (t)tC (t)X C1Qt~a dXLQ lun LINlL

C LINLL CNlGt (~ClLI~ NU dLL~ LL~QL ra~tnlL (tC x) N CXNL Nt Qmcrq tnt LQIILCU lCLcJ1 NU ~t~ClUQ

x (1- i + zx) tC --ZuePIB x-yJ

x (1- ztC + ox)x -ZtnnJIemiddot tC =q

L umCl NU lNrLC~ tnt LLnU CC~ tntc tnt lL~trML (QQG~ IiCU NUL qL~a)

UNLl NU UGUUlU ClQt CLitQ~c1L adct 5ClL f = Lf l f- = 1 bull

C rr~u tnL UXlt cJCLLt 1 lC1Ql 0 =l LcJltGClLX mt LtnU L~

C LNQ N~l ucr~lU LULlU L~li~CLUl

N LNl tnl Nd QIt

calLt lGGlLmiddot

WalCl NU QClLXU ldalLq NtnL UCGhU tnlllU ucr~lU LN4l X~ClU CClQGLCllL NOO l~tN lZlL U~liLr~

r 1) ruUlU LUCr~lU LCNlU

LCll- mIlUQ LUt lUtQLq LtnNQ tLlllUCUlI CLI LlllCllU mlct 1It ~LQ

atL 11 tntllll CNLCft LlllNtlU LCNlU

(CltCLN -tUcIllLC~LLI ~KC~LI) CU(L CLIllLILl ~KCrJJ NI

CLlL C - WOI6Z GLLG U ClClGLLtL

Iil-~ 7jJ

4f+~sx x llIBllIe e

(LG~ al~ lLILtNL

t rcu arc lUU~U I ex eNOlL Iraquo III~I UalCL NLI WI (J)x Claca dtLrO LUCL UNLL

C UNLL CNLGt N~CLU NU dLL~ llLQl CelalLL (t x) N QtNL NUlQalCto m~ lQLILCU LCLciL NU tCLUO

x (1 - (t + zx) I - I trellIemiddot x- =j

x (1- zt + t X ) x-Itml~Ie t =q

I umCl NU lNtLCL ol~ LLOlU CC~ m~c m lL~rCldl (QOGd LiCLL NUL LQdLdJ)

UNLl NU lLUGUUlU C1Ql CLtQdL adcL selL f = 1f L f- = 1f bull

C n~ alL UrtLtr dCLLI 1f lClCZl 0 =1 ldLtGrClLKl ol LLOlU LrN

C lNO N~L LLlCtrLU lUrLLU LrAlCLUl N LLNL OlL Nd lQAi

CQlL lLGGL umCL NLI Q(lLrtU LdlZlLrO NmL LlCClrU OlalU lUCtLU LNl rAlCLU CClQGLClLLL NGO L~ fllLl UtLrr _ ]

f I) rumu LLlCtrLU lCNLU

llQl- alllUO lUA~ lUQrLrO LmNdJ ~lmuQt11 CLl Lt11rQLU mllct It rLO

ml LIl Ol~Llt QNLCLI ll1N~lU LCNLU

(~CLN UlfilLClll LliCd)

CurL CLalllll LAtd~ Nj

ClLLIL C - IE)0l6( Gt-LG U ClClGLLtL

c mLClQl NU l- s~uHonnu m ltlCILCU CUmll (kx) lNU dll lLlUl ll

t( ULL [dlllU LmCU m lUCIlCU LUl llKltLU mLLI

eNml 0 lt poundox UKlrQ NU liM LGCtLU me mu LNlCclJlU

Z fltlj Oltl t O=ljO=l

Ln~Q l CL[llL mLCUUlQ m tlNrLrL uuac Co LA = i = UhNL NU l cmrl LUdLO

r- Lrrcu UL dlLL nne me g mlNb NLl-mb

mdceuQ C LLNl mlb[tildL me LUaLCU UIDnl NU LG1eUl CUlU LrLlNW me LNCLrL

N cun NU UNCLrlL me LU1LCU lIJOCLLL NU LNLLO umuo mlr

lOdCLa lleGl llKlL If fir [lLl[Q Nreuo KUllQ uLmUu LlGGeLgt ere l llmL G(GGic Q~UQL Oltf

(T1fI) 1j1IUl =

~LULliar -Cll lcClclI lCllIcCclI Cll L~rCdL L1~lIl cmiddot lL~l l1liltL Il rGlILlI CNalL ClallICl(l~Q CClClLSlI LcmLO LCllC-4lI cruLU ~tcdlI uo

ClLLOmiddot

~ lL~l mC~alL ClmUC-UllQ CClClL~[ LdalLQ LLt4L m~ LlGG4L LdnClI CllttlI 41CLltllI

(v-IH=(l-= fl~)ld

(11 +1)1- (1 fl~)ld v) rum ClliLCU m~ 1laquo N (lLlrQ ttL~q meL CllCltltQ 1amlI ~G lG~lmiddotC

Cu0 l ff tLl4 (Llim dCll) tCLL -[

lt If I

C Cl~l ~lI rdlLllI mLL LcUna~ CGltaxL m~ ff ltUUl NU llIl LLrL Cttl4llI ff cCll (Llim t Cmiddot L~a llIlDU lI4Ld t~dLlllCl~ll LClGlLCll I ~ CUUl ~lI LL tClaL alIlLClamNlI LClOO L

Cl IC ~u LLfim l If flL UXlt

Clllll)L 1l ClbullbullIClI Nl LG4~lI LClt(~Xlil C~LC~lQU nLltQ ldOClCllLU CdfllLlU a~~l c~mL f1 pound) rlIm LClfllL~ lC~ [(lj-Ul [)gJqtreHW-middot~middot

-~~

ex DJlllJ nlPOJlJ lnJD 2002 ex TlJ1TJ

IPll9EllJ lUn 91l9

n1cGil mlC(Wil ]JJ1C(13 OJ1poundll]J 1JJJ Dr I]J lJ1i1[J] nm[J]l 9TJ [J]nn[J]ill DC(poundlll DlTlnnil nllJpoundll OJllll -113m

nlll1N T991i1 non mlJ~nC(J il~pn1J91N n]J] lllng 1

D1TIil n] nn[JJl nC( AlP DOJT100ilJ DilljiJn13 ilN191il Tml DPOJ 1 1~ IJjin 1nrJ 1S1il DlTIil n]ill 1J mTI13nil moml D~11 Oil UilJ

N 1~ IJjin 1m] 17S1 nJ1 1~11 1 n J1ill - Dn9TlJil 91 D1JJTlOOil nC( Dl1T13 DllTIil nJ mn 1J riD

1~1 lnJI N T]J ( N DOJT11JOil 19U131 ilnT DlTIil nJ 19Dnill ilmilm

n131J91C( ilJ7Sill il]m ilpoundll ilji13PTil 1poundllC( nAlm U)11lJ npoundlll 1)] (C( llJOill npoundlllilpoundll ilA1mil n7SjiJ19 nC( man mN DlTI nJJ 1JJT100 IJ nlJ

illJN13 TTIC( IJ Tji9n nC( ilA1mil nSjiJ19U nllTnw npoundlllil lpoundll ilji13PTil n1C(11[JJ1J mx man (J

n1Jl1n9 ill ilj713PTil IlJ poundllllln nm)WilJ lJ1T

DJnilln Jill lill n13PT nJ1lJ13 nnnJ 2

X =a(x-y)+(x3 +xy2)(1_xl _yl)

y= a(x+y)+(y3 +yx2)(1_x2_y2)

llC(n a ltl1319n [JJ DJlllln UJlllill1JD nJllJUn [JJ OJJpoundllUn nN 1NS13 (C( (xy) 11[JJ13] nUllTil 11ji nC( nlJlN 191NJ

ilm il7Sjil19Jil 11J1319 1i1U 1J DC( i117Sji1lrJ 1T nJllJ13J nWn1n13 DC(n (] i1Tc(9 1JlJ13 IJJ DIllPpoundllil nC( 11C(n i1A10

m1C(19 nllPT11C(ljiJ 1ll1DIllJ lTlPill lJ1n ilC(lllil ~PDO IJI il1Dil

r2 =x2+ i~ I

y I 0= arctanshy

x I ir=ix+yY I

1 ( )0

0 =-v--xyrshy

I

nlN)1 nlltlJil]Nl n11tmUj7~ nJllJD 3

ilU1J1Nl (E) nll1JnUj7~ ilDlJ1~D nJJlm 0]111] nJ1UD 0]111] IUJ (I) nlTrpJilPN

nrDlIJ1Nil nm IUJ lJsmnn lil JSj7 IUJ nrmTil nlN11UJDn nN mUJl (N 1mJ O]lT1] ]UJ IJ lJ On9Pun OlUJj7il lUJNJ INPln ITlDJ

nll]) ilS0j71n JDT WEI 1 WrE nDlJ1Nil rJ1 Wn 1 WEE nil nr01JlNil Hi 1 HE DlJj7 J1STI Oj7 DI UP nrm7J1Nil nuJ7 l1 1 lE Oil nlDlJ1Nil

OlnD19il JllJ lUlJ (J Wu = 0 WEE = 1

wE=-WEI =1 HI =-HE =-10

nN 11j7TIl nrlJstlOil nlT1PJn nN 1NSD OJSTIil JTI1DJ nlPj71m nN llS

(L) 1m ilSilJ19J lnJJUJ ilTIlm j7 nN1 r91N lE

mm IUJ ilSj7J19J npmJlNil nUJ IUJ lil JSi7 nN OTIJU 191NJ llS (l

nlJ11JT P OlJ T99ln nun 4

nJ 191NJ lTIJJ t IJ lUJNJ l11JT nllJn P nJl T99ln nan m1m

Pr(jJl =plusmn1)=+ 1]Uil 191 1n= f shy

ill1J OE19PUil Olillj7n n~ Nlj7N 191NJ OJnm Pr(Jij (new) =Jij (old)) = a

IPr(JIj(new) 0) = I-a nUJlil lUJcD UJlJlillJUllJsmTI nNl qhf IJPUil 1m lJsmDil nN uUJn (N I

I

1 lllJTJ nNsm j

it) nJJnnm ntlJTIil ITIUPTIil P ilUJ illU1I nlN un nrJN nlTDJ lNlil (J I I

aNP =-- Nli1 ilJS

max 21n N I(0-1-0 llJU) NJil J11ilJ lUJTInUJil I I i

10 ~ 02 I

1 f --r 1 cr----- I IPr(-b lt X lt co) = e rr dx 1----e rr I I~27r02 -b J27r b

I

~rf-

sooUC)

N D]lllJ n1nrnlJ lnJ1] 2003 IN 1)]11]

IT]il Tn TTl TPl19tJ1J llJn 91l9

nmJil mn~UJil lJJ1NlJ UJllID IlJ 1]lJ OT IlJ pmUJ nlDID1 qiJ [JJDnIDil7 TI~UJ1 OTDnil nllJUJ UJllID -llJTil

11 nTPJD na ]1]1 IT1n 1

ilNllUJlJil nN TIjlJ 1111] lID ilJlJDlJil IN~nrn9 1 ilUJU lID ~lJlJlTmJ dv

C-=-gL(v-vL)+A(v-vJ2 +lUl dt

J1~n TIlT Nln larl Jln DWD A llUil 1(0 (leak) ilPTil nlJm gL 1Jjil C l(oNJ

illl~) ilN11UJnil nN J1nJ1(o9NID lNlil N

dV shyC-=Av2+IUl dt

v=v-v _kmiddot I = I - 1 lillllJ -- L lA ct - Ul -4A ~I

lmJ~ ilm lrrt lt 0 11JlJ ilPlJPTil 1m nJillil nlllpJ lilD J

8m 1mJ 1TJnlJ v~) DJ Pl1 v~) ill 1N1i1 v(O) =0 t=0 J1 lUIgt 0 -(0 11m l

b dxltI--2=arctan(b)- arctan(a) 11lOJNil 11m)

(Jl+x

1]1(0 Tun Nm 1m ilDJ 11JlJJ -co ID1lJ nN UlJJljllTJnlJ v (0 lnN T

i

il11~il 7lJJ F UJ 1N1il (j = F(Ia)) ler I[J] il~jlJ18J l~il J~jI N1ilD il I

I I

F(Irrt)=K~lct-IIh lUI gt~th o otherrVlse

nJllJlJil Iill lrlJ1JiI lJ 1)lJJiI) KIth lmNJ I i i

I I

TI99m nan 2

n1g9nil nN Dllm kt ll1JT mJJn p TIlJ 1799ln n(ol i1llnJ

1 IV 11 ) ~UI 111 =- ~ s

-- -lJ i i J=I

(Si =plusmn1 ) lNJJil lillJi1 nlllJ9 1(0 D]lilJlnil lismDil (s) l[JJNJ

nlN)1 nlltlJil]Nl n11tmUj7~ nJllJD 3

ilU1J1Nl (E) nll1JnUj7~ ilDlJ1~D nJJlm 0]111] nJ1UD 0]111] IUJ (I) nlTrpJilPN

nrDlIJ1Nil nm IUJ lJsmnn lil JSj7 IUJ nrmTil nlN11UJDn nN mUJl (N 1mJ O]lT1] ]UJ IJ lJ On9Pun OlUJj7il lUJNJ INPln ITlDJ

nll]) ilS0j71n JDT WEI 1 WrE nDlJ1Nil rJ1 Wn 1 WEE nil nr01JlNil Hi 1 HE DlJj7 J1STI Oj7 DI UP nrm7J1Nil nuJ7 l1 1 lE Oil nlDlJ1Nil

OlnD19il JllJ lUlJ (J Wu = 0 WEE = 1

wE=-WEI =1 HI =-HE =-10

nN 11j7TIl nrlJstlOil nlT1PJn nN 1NSD OJSTIil JTI1DJ nlPj71m nN llS

(L) 1m ilSilJ19J lnJJUJ ilTIlm j7 nN1 r91N lE

mm IUJ ilSj7J19J npmJlNil nUJ IUJ lil JSi7 nN OTIJU 191NJ llS (l

nlJ11JT P OlJ T99ln nun 4

nJ 191NJ lTIJJ t IJ lUJNJ l11JT nllJn P nJl T99ln nan m1m

Pr(jJl =plusmn1)=+ 1]Uil 191 1n= f shy

ill1J OE19PUil Olillj7n n~ Nlj7N 191NJ OJnm Pr(Jij (new) =Jij (old)) = a

IPr(JIj(new) 0) = I-a nUJlil lUJcD UJlJlillJUllJsmTI nNl qhf IJPUil 1m lJsmDil nN uUJn (N I

I

1 lllJTJ nNsm j

it) nJJnnm ntlJTIil ITIUPTIil P ilUJ illU1I nlN un nrJN nlTDJ lNlil (J I I

aNP =-- Nli1 ilJS

max 21n N I(0-1-0 llJU) NJil J11ilJ lUJTInUJil I I i

10 ~ 02 I

1 f --r 1 cr----- I IPr(-b lt X lt co) = e rr dx 1----e rr I I~27r02 -b J27r b

I

~rf-

sooUC)

N D]lllJ n1nrnlJ lnJ1] 2003 IN 1)]11]

IT]il Tn TTl TPl19tJ1J llJn 91l9

nmJil mn~UJil lJJ1NlJ UJllID IlJ 1]lJ OT IlJ pmUJ nlDID1 qiJ [JJDnIDil7 TI~UJ1 OTDnil nllJUJ UJllID -llJTil

11 nTPJD na ]1]1 IT1n 1

ilNllUJlJil nN TIjlJ 1111] lID ilJlJDlJil IN~nrn9 1 ilUJU lID ~lJlJlTmJ dv

C-=-gL(v-vL)+A(v-vJ2 +lUl dt

J1~n TIlT Nln larl Jln DWD A llUil 1(0 (leak) ilPTil nlJm gL 1Jjil C l(oNJ

illl~) ilN11UJnil nN J1nJ1(o9NID lNlil N

dV shyC-=Av2+IUl dt

v=v-v _kmiddot I = I - 1 lillllJ -- L lA ct - Ul -4A ~I

lmJ~ ilm lrrt lt 0 11JlJ ilPlJPTil 1m nJillil nlllpJ lilD J

8m 1mJ 1TJnlJ v~) DJ Pl1 v~) ill 1N1i1 v(O) =0 t=0 J1 lUIgt 0 -(0 11m l

b dxltI--2=arctan(b)- arctan(a) 11lOJNil 11m)

(Jl+x

1]1(0 Tun Nm 1m ilDJ 11JlJJ -co ID1lJ nN UlJJljllTJnlJ v (0 lnN T

i

il11~il 7lJJ F UJ 1N1il (j = F(Ia)) ler I[J] il~jlJ18J l~il J~jI N1ilD il I

I I

F(Irrt)=K~lct-IIh lUI gt~th o otherrVlse

nJllJlJil Iill lrlJ1JiI lJ 1)lJJiI) KIth lmNJ I i i

I I

TI99m nan 2

n1g9nil nN Dllm kt ll1JT mJJn p TIlJ 1799ln n(ol i1llnJ

1 IV 11 ) ~UI 111 =- ~ s

-- -lJ i i J=I

(Si =plusmn1 ) lNJJil lillJi1 nlllJ9 1(0 D]lilJlnil lismDil (s) l[JJNJ

~rf-

sooUC)

N D]lllJ n1nrnlJ lnJ1] 2003 IN 1)]11]

IT]il Tn TTl TPl19tJ1J llJn 91l9

nmJil mn~UJil lJJ1NlJ UJllID IlJ 1]lJ OT IlJ pmUJ nlDID1 qiJ [JJDnIDil7 TI~UJ1 OTDnil nllJUJ UJllID -llJTil

11 nTPJD na ]1]1 IT1n 1

ilNllUJlJil nN TIjlJ 1111] lID ilJlJDlJil IN~nrn9 1 ilUJU lID ~lJlJlTmJ dv

C-=-gL(v-vL)+A(v-vJ2 +lUl dt

J1~n TIlT Nln larl Jln DWD A llUil 1(0 (leak) ilPTil nlJm gL 1Jjil C l(oNJ

illl~) ilN11UJnil nN J1nJ1(o9NID lNlil N

dV shyC-=Av2+IUl dt

v=v-v _kmiddot I = I - 1 lillllJ -- L lA ct - Ul -4A ~I

lmJ~ ilm lrrt lt 0 11JlJ ilPlJPTil 1m nJillil nlllpJ lilD J

8m 1mJ 1TJnlJ v~) DJ Pl1 v~) ill 1N1i1 v(O) =0 t=0 J1 lUIgt 0 -(0 11m l

b dxltI--2=arctan(b)- arctan(a) 11lOJNil 11m)

(Jl+x

1]1(0 Tun Nm 1m ilDJ 11JlJJ -co ID1lJ nN UlJJljllTJnlJ v (0 lnN T

i

il11~il 7lJJ F UJ 1N1il (j = F(Ia)) ler I[J] il~jlJ18J l~il J~jI N1ilD il I

I I

F(Irrt)=K~lct-IIh lUI gt~th o otherrVlse

nJllJlJil Iill lrlJ1JiI lJ 1)lJJiI) KIth lmNJ I i i

I I

TI99m nan 2

n1g9nil nN Dllm kt ll1JT mJJn p TIlJ 1799ln n(ol i1llnJ

1 IV 11 ) ~UI 111 =- ~ s

-- -lJ i i J=I

(Si =plusmn1 ) lNJJil lillJi1 nlllJ9 1(0 D]lilJlnil lismDil (s) l[JJNJ

291 004 iOWl1 11 ill I~ ml1Wi1 nw

ml71U lVlWl mlltw 3 im) IU

tl1 rrlnll 11~1l11U1 1 TJi nmilT 2P C17J~ (B) JJill1illJ i l1UlT P O17JUil (A) j))ill1WiJ

11 ill1ro jlW OilUjl-r l1Ii~tll (C) illUin Tlilli OiC

(05) -rlU miJJiOilJ Jff =J 11lt Jff =J (C) l1IUiJ ki l mJilTil l tV TllJ n~JCil ilOPilil P -r ilil

I7)N~ 1~P7) 2 Ol11tlll Jtll IV ro37ll jmnJ

x = -xmiddot sign(x) - y

y = -ymiddotsign(x)+x (xgtO xltO) i1illilil ~Xn JtllJ ilim 1jl111( TllJiJilTlI( li~

yeO) = 1 x(O)=O ilTlilil OTll mnl1)1li1TlI( iKI1

(xy 1tllilJ iliil]1ilTlI( 1C)

(lUllll 117 gt Jit7 Cl xy )

11N~ n~ItIXtI=N 3 1=1 17Jp K1il Ol~Jil Cim11l11ro C=1 R=l 017 JC11 K1 W RC ll lro K

nl1ilil 7W lllTJ ml1il me 1K

(v(O)=O ) v(t) =_t- Jjil K r170ll 11mil om ilJli11l1J OUiill) llT 111in iiJllI1lJ m1XiJ J 3600

R 1 C tv Olil7i1 mil Ogti il

bull ~2 TlmJl1iiil 17 0iC1Cil (i=12) Ct R Oi~Ci)il 017 0l1l Jill 017l1li17l ilJro l

ex) gt C Rj Rugt 0 11=1 12 = 0 lro

(g = IT) ilJ1Wl1ill1llt 11JOil 11 1170J lgt l17W 1Til l1li17llil 11iTliJ mrh l1lJ OKil R

m~N=1-N 1~P7) 4 Tlli17llil imro

~=f(v)-w bull W= bmiddot(V-fW)

3f(-l lt v lt1) = 2v- v itvlltJ

f(v gt 1)=1

f(vlt -1)=-1

b=4 0lt( i1J37

( 11l 0J1ill 0J17 i1137 TllTKgtil InlJ illlim 1v 11K I1UJil 11K JlUn 1(

y ill OllUil 0ll1n11J DTlJ1IJ um I1JlUill1myJ 11K ll1ln J

ilXii1)1Jil i1)lgtJ m711J l1lillil mi1pJ 11K liX l

ilnliill

TI1pnD ~il 1PJ l~lil iiiWD 11WJ mil OiTJi1 nix TIJJJ1iil m~lWnil TIJ1JJD ilD N TOUDil mmWUD (Olillil IP17Wil)

J In)i1) mu=(mmmQO) iJW J~D1 m il~ ilJJ1ijlil i1~llillDil JlN l1JP J

(t~ ON -+ 0)

T -+ 0 lWNJ 111 ~li11J l)~rlU ED p~ i1T JllJlD) jI9UD Jl1l1ll19D13Jill HXlil J

nJ17JN nUll lID i1VTlPT 3

lJ mtnilD nilllill[JJ iljiDP1n m JSiJ ill DilTI 1TIN IJ[JJ D)l1JN IPJ11lJ IW n[JJl ilJ1nJ ilNl1illTIil

dm = -m+ gel)dt

n11llD gil~PJ19m Jgt 0 ]=Jmiddotm+Jerr Jl~nil1 DJ9il mIn I[JJ DlJU Nln lmTillWNJ

0 1lt0 gel) == Ir nm

-vI Igt 0

lat lID il~PJ19J 1illW nlJ~J mn iljiDP1il lID nJillil illnPJ ilN lN~D ~

lD11ill9N 1110 ilTN1 DTlJDil nN ITJUil - TIIJ13OJ Nil nIDlil Jut I[JJ DlUD OmnJ J

7111JT m~D mDlilill

mD11Jl~ nm 1m i1i7DPT 4

DJlllJil IJ lill lil J~P OlltPJilPNl Oll1313OjiN OJ11lJ lill nJlllD ilJ1m

m O1113)i1JNil Iill1 mE N1il iJllrlnDj7NilI

nlNl1illDil JJ m~mD nJlJJDil iill iliDP1il

dm- E ---- = -mE +JEEmE + JElm +1E

dt dm1-- =-m[ +JIIm[ +JIEmE+I[dt

J lJ =OJEE =Jz =-JEI =l-II =+J E =10 ill 11m

nlTN9il )nlDJ illJIjilJil nN l~ ~

7ili7OJ1il lill n)[JJil n1ljiJ NilD )

a == ~ I[JJ il~jlJl9J nJlllTIil till nTINJ1il il11ilJnilJ 111 1

il)l[JJ illli1Jnilil Uil) a tal DJl[JJ DDlnn 11111 m~) nNl m~~) nN nDJD 19HD 1S 1 (nnlJN

~Il7nJJ7J

I I fq +ImEI + 3OI33J+ rm -= rm 3l i I lL~rCZrcJ lll~ lCZlLCl CZtn~LU ~~ ~L~ lCZlllU~LUI I

~~l l~ 3m L- 1m tlImCUi I I I pound) nml CZIDel tn~ n~Llrdl NdO~QCll~~tI LN~r~cQll4C att 4Lr tn~ ~ ~Ul czJ l~LC~lC~Ll

I r I~L lll- m LllL ~GO ttnU~ cuncJ~ I I (mlt rm)

t ct~l ~l lCUllLL~ll L4tChll IdLtLLl ~l 1lLrmruLU tlczl tn~ CXt (0 0 zID tm) = lim (Lal~tQ 1ampALctQ) ClCltnL~l ClOQLmiddot

~ CZl CZIDCl lcunL~LU IcJLtl ~ll L~4cL tn~ IcLCZctLrQ L~~ll L~l CcL ~~ CZl-Itl

tLlAl ltSgt (OUlll ltsgt ICZCZLXL LULCZLl4tCZ1 tn~ Itl4LLl LtcOO t+ = S) Z) GLCZct~C rim tU1lPIQgdoH CZLCLL~tl CUGrGl tJ LtCIl llCLLl ~ Ltd CZXt lGL4~LU

L Utntl ~U LNtlC1 ~ LLtnl tc~ tntt ln4 LL~rCZ4d (tlOCkd roL ~UL CZc~tl) UNLL W IllIGUULU cd tL4tCZrdl czdtt4- 6oL SIt = l[ l Sl- = l[

C tt4U tnLL IUlr Cru l[ LtlCZl 0 = J dLrC~ru~ ~ lLtnU ~=

t lIQ ~4l1UtI4LU ~wLU 1rXolIl ~ 1L~L ml1 ~d lcm

tQll~ LGG~

UtntL ~1I qQLrXl Idtn~C NtnL UtQUl mLlllL llICIrJl ~4- tLl tQCZGLQlLJ ~GQ LlA~ auc U~Lt~

llCZ1-tn~LAl tn6lLr ll~CZrL4C LtnampC 4-alLrcztn nl ltl14CZLl tnud l~ LC

tL L m~Lm ~Lt~ ltlULU ltNll

(Ql5l t - pound00e L Le) GLLG unL CltlGLICl( lLmiddot loll COt

tU-t tLAlLIll llit10 ~i

I

TI1pnD ~il 1PJ l~lil iiiWD 11WJ mil OiTJi1 nix TIJJJ1iil m~lWnil TIJ1JJD ilD N TOUDil mmWUD (Olillil IP17Wil)

J In)i1) mu=(mmmQO) iJW J~D1 m il~ ilJJ1ijlil i1~llillDil JlN l1JP J

(t~ ON -+ 0)

T -+ 0 lWNJ 111 ~li11J l)~rlU ED p~ i1T JllJlD) jI9UD Jl1l1ll19D13Jill HXlil J

nJ17JN nUll lID i1VTlPT 3

lJ mtnilD nilllill[JJ iljiDP1n m JSiJ ill DilTI 1TIN IJ[JJ D)l1JN IPJ11lJ IW n[JJl ilJ1nJ ilNl1illTIil

dm = -m+ gel)dt

n11llD gil~PJ19m Jgt 0 ]=Jmiddotm+Jerr Jl~nil1 DJ9il mIn I[JJ DlJU Nln lmTillWNJ

0 1lt0 gel) == Ir nm

-vI Igt 0

lat lID il~PJ19J 1illW nlJ~J mn iljiDP1il lID nJillil illnPJ ilN lN~D ~

lD11ill9N 1110 ilTN1 DTlJDil nN ITJUil - TIIJ13OJ Nil nIDlil Jut I[JJ DlUD OmnJ J

7111JT m~D mDlilill

mD11Jl~ nm 1m i1i7DPT 4

DJlllJil IJ lill lil J~P OlltPJilPNl Oll1313OjiN OJ11lJ lill nJlllD ilJ1m

m O1113)i1JNil Iill1 mE N1il iJllrlnDj7NilI

nlNl1illDil JJ m~mD nJlJJDil iill iliDP1il

dm- E ---- = -mE +JEEmE + JElm +1E

dt dm1-- =-m[ +JIIm[ +JIEmE+I[dt

J lJ =OJEE =Jz =-JEI =l-II =+J E =10 ill 11m

nlTN9il )nlDJ illJIjilJil nN l~ ~

7ili7OJ1il lill n)[JJil n1ljiJ NilD )

a == ~ I[JJ il~jlJl9J nJlllTIil till nTINJ1il il11ilJnilJ 111 1

il)l[JJ illli1Jnilil Uil) a tal DJl[JJ DDlnn 11111 m~) nNl m~~) nN nDJD 19HD 1S 1 (nnlJN

~Il7nJJ7J

I I fq +ImEI + 3OI33J+ rm -= rm 3l i I lL~rCZrcJ lll~ lCZlLCl CZtn~LU ~~ ~L~ lCZlllU~LUI I

~~l l~ 3m L- 1m tlImCUi I I I pound) nml CZIDel tn~ n~Llrdl NdO~QCll~~tI LN~r~cQll4C att 4Lr tn~ ~ ~Ul czJ l~LC~lC~Ll

I r I~L lll- m LllL ~GO ttnU~ cuncJ~ I I (mlt rm)

t ct~l ~l lCUllLL~ll L4tChll IdLtLLl ~l 1lLrmruLU tlczl tn~ CXt (0 0 zID tm) = lim (Lal~tQ 1ampALctQ) ClCltnL~l ClOQLmiddot

~ CZl CZIDCl lcunL~LU IcJLtl ~ll L~4cL tn~ IcLCZctLrQ L~~ll L~l CcL ~~ CZl-Itl

tLlAl ltSgt (OUlll ltsgt ICZCZLXL LULCZLl4tCZ1 tn~ Itl4LLl LtcOO t+ = S) Z) GLCZct~C rim tU1lPIQgdoH CZLCLL~tl CUGrGl tJ LtCIl llCLLl ~ Ltd CZXt lGL4~LU

L Utntl ~U LNtlC1 ~ LLtnl tc~ tntt ln4 LL~rCZ4d (tlOCkd roL ~UL CZc~tl) UNLL W IllIGUULU cd tL4tCZrdl czdtt4- 6oL SIt = l[ l Sl- = l[

C tt4U tnLL IUlr Cru l[ LtlCZl 0 = J dLrC~ru~ ~ lLtnU ~=

t lIQ ~4l1UtI4LU ~wLU 1rXolIl ~ 1L~L ml1 ~d lcm

tQll~ LGG~

UtntL ~1I qQLrXl Idtn~C NtnL UtQUl mLlllL llICIrJl ~4- tLl tQCZGLQlLJ ~GQ LlA~ auc U~Lt~

llCZ1-tn~LAl tn6lLr ll~CZrL4C LtnampC 4-alLrcztn nl ltl14CZLl tnud l~ LC

tL L m~Lm ~Lt~ ltlULU ltNll

(Ql5l t - pound00e L Le) GLLG unL CltlGLICl( lLmiddot loll COt

tU-t tLAlLIll llit10 ~i

I

I I fq +ImEI + 3OI33J+ rm -= rm 3l i I lL~rCZrcJ lll~ lCZlLCl CZtn~LU ~~ ~L~ lCZlllU~LUI I

~~l l~ 3m L- 1m tlImCUi I I I pound) nml CZIDel tn~ n~Llrdl NdO~QCll~~tI LN~r~cQll4C att 4Lr tn~ ~ ~Ul czJ l~LC~lC~Ll

I r I~L lll- m LllL ~GO ttnU~ cuncJ~ I I (mlt rm)

t ct~l ~l lCUllLL~ll L4tChll IdLtLLl ~l 1lLrmruLU tlczl tn~ CXt (0 0 zID tm) = lim (Lal~tQ 1ampALctQ) ClCltnL~l ClOQLmiddot

~ CZl CZIDCl lcunL~LU IcJLtl ~ll L~4cL tn~ IcLCZctLrQ L~~ll L~l CcL ~~ CZl-Itl

tLlAl ltSgt (OUlll ltsgt ICZCZLXL LULCZLl4tCZ1 tn~ Itl4LLl LtcOO t+ = S) Z) GLCZct~C rim tU1lPIQgdoH CZLCLL~tl CUGrGl tJ LtCIl llCLLl ~ Ltd CZXt lGL4~LU

L Utntl ~U LNtlC1 ~ LLtnl tc~ tntt ln4 LL~rCZ4d (tlOCkd roL ~UL CZc~tl) UNLL W IllIGUULU cd tL4tCZrdl czdtt4- 6oL SIt = l[ l Sl- = l[

C tt4U tnLL IUlr Cru l[ LtlCZl 0 = J dLrC~ru~ ~ lLtnU ~=

t lIQ ~4l1UtI4LU ~wLU 1rXolIl ~ 1L~L ml1 ~d lcm

tQll~ LGG~

UtntL ~1I qQLrXl Idtn~C NtnL UtQUl mLlllL llICIrJl ~4- tLl tQCZGLQlLJ ~GQ LlA~ auc U~Lt~

llCZ1-tn~LAl tn6lLr ll~CZrL4C LtnampC 4-alLrcztn nl ltl14CZLl tnud l~ LC

tL L m~Lm ~Lt~ ltlULU ltNll

(Ql5l t - pound00e L Le) GLLG unL CltlGLICl( lLmiddot loll COt

tU-t tLAlLIll llit10 ~i

I

I i~l~P liliil ii~TiJ

iili in ~1 bullil~nE)tiil jilii E)ii

(27 72003 - 1i3i1))

ii1ll1 ii17liVii slilil Wi71i7 7raquo iilii

Oi 717 Pkii17 Ji1tj~i ]11 lVliiWP OlU7i OI7)7nJ 1iU7W 1i)W- j7)ii

1 717 OllO JlOliiJi( ilinlil ililitlDil iliil bull Olntl ilimlil illi) 71i) iI l-iP 1 il1iJ1 n1t11i1iilii

tama = bull ma + get (ha) a= EI

a Ol~ll1 iIi tl7j bull hltt a 07l11 iIi jilii SlOp - ta bull a iiO7l1l1 iIi ii ltV - IDa

hE = JEEmE - JEImI+ hOE

hI = - JrrDlJ + JIEmE + hOr

p Itll a~ l Jail gt0

gz(x) x xgtO gr(x) =0 xlt0 gs(x) = -Vx xgt 0 ga = 0 xlt 0

illW-J ii111jiD iiintji nl It7iJ (mamr) iiii7il IliJgt7P71lii nit 1i1 hdegI = 0 -10 Oiil7)

717 i7)17 ilO~ i7) iltiiii 7tV O7tJOOii O37)ii i)07)1 ill1 mE( hDE) ii-ijiJ1ilK n~~

bi1D7) (0117n 71 Oii1O IlllOOii

7iZ jijtOl iliin iiit)il JWI7ri01l7 nntu~ tuW i ilnui IlliiPl 7tV il17uii ill mJiJ 1 I

trraquo tE -111 Itt

Ilil11Wil1 ~1 7iJ ilU1l 017)7) Oi1OlilK Cllitl ltV tu ijnJiii 2 i I1 mlbull = bull ml + [ - Im2 +11]+

I I

tm2=- m2 + [ bull Iml + IzJ+ I jI

Clll1J1 Ii) OliIiiii Otl7ji1 01 AAiPiliii 7W ilioi iiilP t1i t iW-l i xgtO ii17 [xJ+= x I

mnlt [x]+ = 0

III 12 7iv ilpJllgt jililT-ll iii-jil 1m iijl7)Ji1 7i7 il1iWlli roiiiii iliiijiJ ii l~7) l Imi~1 i 7g ml~uij ill 1gt0 ii7~ltlO li ngt1iiilii IJ101Yll tlli1il iitl J

JltO- JgtO 0 (II 12 )ijiV~l nniiiljj 7W mil) I I II I

1nl1OI j)liTi 111( ITI l11TI(ITT lmZJll11J~jiil- 111( i K a == rIiTE w iijiJl1) l1YI17ZlTT tV l17lJii l1Uill1il il11 1

TTT rlP))l TTiOli1 11K t1lJO 1l1Kl liKil il~ iJK nlWTT mlpl a ill C)il iirK i1ll l

l11TI()i lni))1 17011 i 7l

(limit cycle) J1 i1m1l 101l TTT iijZJl CjI C 7I i

iI lxj Ci1~Iill( Cl1i1J NI-l o~~DiiK OJ1ill Ns -Zl rcrJiW C11i1J l1TUi (4 TT1W1II1U CP1ll1lVO Cl1iUllZl inK 7liIi (a =EI) mai

t ~~~ ==- - 141~ + ~oc C~~ ) iWlO rx Xgtopound 0 X lt 0

gr =- x xgto xlt 00

Ol1il1 JW 7l rll l1U1WTT 11101l1KTT1l Cl1i1l JW 7l11 0tlJ0 CiWji C1ljiti711m

iii C11111li171ll OtmlOTT CiWjil igt 0ilJTTllot OJliCI lU7 11 K7 lK Ciltt)OjKj lji1) Oilt)OPNTT Cl1i1lTT 11l 1nlotgt JaIl ~ t)JiO-DOElTTl lJ0-iiilTT11i1J1 11017l1Kl

110

l1iTl71 MI ME m017gt11(1 11ti7l C~~1l1l ii Itj 7W iij1Il1ii 111K11W1ll1lot O1ll lot

ho-l JcrEJ~p OiD1liJii 0J1iUTT l1D1m l1Jill I- i11tU ml1117 mo1il1lot 1l117 rl Jail it11ligt1 W 71 1

110 U7 ii~PJ1l ijil1lJ1 7117 nlW1 l11i1jil i001ll m1 2- I11U7 0i1OPK1 illll7 m1jl 7117 1117ICI l i1l1 ilI7Jlot 11l l

m~tclot mljl11l C0117 Clotlli iU Clot 1

1-rn~x-rJ

i

I I II

I I I

i

I

I I i

I

I I I

I

I I I I

I I I II I I I I I I II

fa 0 0 IO a [ shy

0 [- a110 c t-IL 0 a

CLI7t ( S ClltLlQ CINL~(C t +J CI(I 4CChCt C~iCll(1l CCLIl UdRLC LtNL

t ~~ C1~C llGl tlLLO QCl=CI[j~lr~ IiS tc~ l cmiddot tlCtL ~l Qmlllll lLtCll amplL tm 1m (LCGLl CIl CLLtLl lGI~LU CllLCU)

lCLll mtIm (Lcn CClllUal L~mLr ~czmiJl ~ LLNL malr lCLtrlU lCC c- 0=1 ~oL c (lttkI LNO tladtt ral~Ll (CLe NO tltO~Ga

mrd 1= 9 tQrCLr -g- I=~ QQLrl dc1lL~Cl Lt il4 Cll PIQgdoH cliru ~~allr I=~ COICl ll=ltllLrctl

pound rLl1ClLCl (11 N n~Llr~c cr~40 alC aICCIC illl1 lCLmu t~ l~ tNcll

tCLL CC+-l OlL ZI lt roIl elxt lL nL lgtll c- L==I c1lc Lo CGilLCMl ua4QJ 0 lt toIrr au co elf-C L

c c- ()=I cJc 4L al tlurc LIN ottlllw ardtCl (I1mL lgtJ OZI=Ir alo

I I

j

J

r I

10 t 01 L- 01

0

o ~J

tmiddott (4-x)T= ~

tff + cy = lJi I XI If ~jB = Bl I I I II i I urru tCt aalGI umNtU ULCtL tULCllL cmlULm CdlNlLh[CllLI GleNLlllII I

mni LINLl NU UffiL[lLIO cct urrCL GNUI C) UNO UULumLI tclITLCU II CLGLLdKLUi NO cl UUL GLUGlL UCLGLLdKIU LUU

I

i CNLGl NLClUL NU dLLL UlLLUU CULrnlL (AX)j

N) UKNl NU UumC[10 mt UUITLCU atlL uaLCLO UffiL(LO mt UGLUGlL E UNLli

( - tX-r)(txA + t9+(K+x)t1 =~

(tA- tX-r)(tAx + (x) + (K-x)e= c

urL CUffiGITU UUIm ITt Uh[[hdu LUGUUrlll C) Lmm NU UmltNlU UhWdU me ULmu mrnuu UGlrtiKdl UNrulU NU UGllLl ct NUl UNCLLU mt ct DGllUGl CCLU ULtLO NUL LmaL NU GlrdKLU UNrLrLU mt ULmu LUQCILL N) trl Lmu rLLUfLO N[tlrioU NrnL UhCUdU mtu UlCLtU tUKCU NlGGlLUtLU (Uuruu rnU06L CUI UULtLO lUU tUOGL UOllll[Gldl - N ) ITl N ~C tUL Uillmiddot cm cl uru~1 CUI UUl~Ln CllLrlO NU UOGllUGlLn t6L UITlGUO - mlC U ~ ~LKlL lCtUL LKlL tLlUL utitt hLll N CUD un LLKIO tmrJlU UUUUlLI cL mclu UULtLO ULKlL CLlUL udtt KILl LI

COLLO tLULlL lLGlNl uutdmLo ct UOGlll[QLO tlLr NU LmLUU CUI lUltLO

~ Guul tITLLU NlGGlIULlhLl tNUKCUU UDU LLGGLel Nr~lrLu

Ulul- meLm mcuu lUtUI1LO LmNIO tUffiuurn clb LffilUlU mULcl at LlO an a~ mtlm UNLta lffiNtllI lCNlU

GLl6 lHlL rLGlGLLI[l alal N I ZOO

[reul [LmLlLLl [lILl[l[l N iJ

1nl1OI j)liTi 111( ITI l11TI(ITT lmZJll11J~jiil- 111( i K a == rIiTE w iijiJl1) l1YI17ZlTT tV l17lJii l1Uill1il il11 1

TTT rlP))l TTiOli1 11K t1lJO 1l1Kl liKil il~ iJK nlWTT mlpl a ill C)il iirK i1ll l

l11TI()i lni))1 17011 i 7l

(limit cycle) J1 i1m1l 101l TTT iijZJl CjI C 7I i

iI lxj Ci1~Iill( Cl1i1J NI-l o~~DiiK OJ1ill Ns -Zl rcrJiW C11i1J l1TUi (4 TT1W1II1U CP1ll1lVO Cl1iUllZl inK 7liIi (a =EI) mai

t ~~~ ==- - 141~ + ~oc C~~ ) iWlO rx Xgtopound 0 X lt 0

gr =- x xgto xlt 00

Ol1il1 JW 7l rll l1U1WTT 11101l1KTT1l Cl1i1l JW 7l11 0tlJ0 CiWji C1ljiti711m

iii C11111li171ll OtmlOTT CiWjil igt 0ilJTTllot OJliCI lU7 11 K7 lK Ciltt)OjKj lji1) Oilt)OPNTT Cl1i1lTT 11l 1nlotgt JaIl ~ t)JiO-DOElTTl lJ0-iiilTT11i1J1 11017l1Kl

110

l1iTl71 MI ME m017gt11(1 11ti7l C~~1l1l ii Itj 7W iij1Il1ii 111K11W1ll1lot O1ll lot

ho-l JcrEJ~p OiD1liJii 0J1iUTT l1D1m l1Jill I- i11tU ml1117 mo1il1lot 1l117 rl Jail it11ligt1 W 71 1

110 U7 ii~PJ1l ijil1lJ1 7117 nlW1 l11i1jil i001ll m1 2- I11U7 0i1OPK1 illll7 m1jl 7117 1117ICI l i1l1 ilI7Jlot 11l l

m~tclot mljl11l C0117 Clotlli iU Clot 1

1-rn~x-rJ

i

I I II

I I I

i

I

I I i

I

I I I

I

I I I I

I I I II I I I I I I II

fa 0 0 IO a [ shy

0 [- a110 c t-IL 0 a

CLI7t ( S ClltLlQ CINL~(C t +J CI(I 4CChCt C~iCll(1l CCLIl UdRLC LtNL

t ~~ C1~C llGl tlLLO QCl=CI[j~lr~ IiS tc~ l cmiddot tlCtL ~l Qmlllll lLtCll amplL tm 1m (LCGLl CIl CLLtLl lGI~LU CllLCU)

lCLll mtIm (Lcn CClllUal L~mLr ~czmiJl ~ LLNL malr lCLtrlU lCC c- 0=1 ~oL c (lttkI LNO tladtt ral~Ll (CLe NO tltO~Ga

mrd 1= 9 tQrCLr -g- I=~ QQLrl dc1lL~Cl Lt il4 Cll PIQgdoH cliru ~~allr I=~ COICl ll=ltllLrctl

pound rLl1ClLCl (11 N n~Llr~c cr~40 alC aICCIC illl1 lCLmu t~ l~ tNcll

tCLL CC+-l OlL ZI lt roIl elxt lL nL lgtll c- L==I c1lc Lo CGilLCMl ua4QJ 0 lt toIrr au co elf-C L

c c- ()=I cJc 4L al tlurc LIN ottlllw ardtCl (I1mL lgtJ OZI=Ir alo

I I

j

J

r I

10 t 01 L- 01

0

o ~J

tmiddott (4-x)T= ~

tff + cy = lJi I XI If ~jB = Bl I I I II i I urru tCt aalGI umNtU ULCtL tULCllL cmlULm CdlNlLh[CllLI GleNLlllII I

mni LINLl NU UffiL[lLIO cct urrCL GNUI C) UNO UULumLI tclITLCU II CLGLLdKLUi NO cl UUL GLUGlL UCLGLLdKIU LUU

I

i CNLGl NLClUL NU dLLL UlLLUU CULrnlL (AX)j

N) UKNl NU UumC[10 mt UUITLCU atlL uaLCLO UffiL(LO mt UGLUGlL E UNLli

( - tX-r)(txA + t9+(K+x)t1 =~

(tA- tX-r)(tAx + (x) + (K-x)e= c

urL CUffiGITU UUIm ITt Uh[[hdu LUGUUrlll C) Lmm NU UmltNlU UhWdU me ULmu mrnuu UGlrtiKdl UNrulU NU UGllLl ct NUl UNCLLU mt ct DGllUGl CCLU ULtLO NUL LmaL NU GlrdKLU UNrLrLU mt ULmu LUQCILL N) trl Lmu rLLUfLO N[tlrioU NrnL UhCUdU mtu UlCLtU tUKCU NlGGlLUtLU (Uuruu rnU06L CUI UULtLO lUU tUOGL UOllll[Gldl - N ) ITl N ~C tUL Uillmiddot cm cl uru~1 CUI UUl~Ln CllLrlO NU UOGllUGlLn t6L UITlGUO - mlC U ~ ~LKlL lCtUL LKlL tLlUL utitt hLll N CUD un LLKIO tmrJlU UUUUlLI cL mclu UULtLO ULKlL CLlUL udtt KILl LI

COLLO tLULlL lLGlNl uutdmLo ct UOGlll[QLO tlLr NU LmLUU CUI lUltLO

~ Guul tITLLU NlGGlIULlhLl tNUKCUU UDU LLGGLel Nr~lrLu

Ulul- meLm mcuu lUtUI1LO LmNIO tUffiuurn clb LffilUlU mULcl at LlO an a~ mtlm UNLta lffiNtllI lCNlU

GLl6 lHlL rLGlGLLI[l alal N I ZOO

[reul [LmLlLLl [lILl[l[l N iJ

I I I I

I I I II I I I I I I II

fa 0 0 IO a [ shy

0 [- a110 c t-IL 0 a

CLI7t ( S ClltLlQ CINL~(C t +J CI(I 4CChCt C~iCll(1l CCLIl UdRLC LtNL

t ~~ C1~C llGl tlLLO QCl=CI[j~lr~ IiS tc~ l cmiddot tlCtL ~l Qmlllll lLtCll amplL tm 1m (LCGLl CIl CLLtLl lGI~LU CllLCU)

lCLll mtIm (Lcn CClllUal L~mLr ~czmiJl ~ LLNL malr lCLtrlU lCC c- 0=1 ~oL c (lttkI LNO tladtt ral~Ll (CLe NO tltO~Ga

mrd 1= 9 tQrCLr -g- I=~ QQLrl dc1lL~Cl Lt il4 Cll PIQgdoH cliru ~~allr I=~ COICl ll=ltllLrctl

pound rLl1ClLCl (11 N n~Llr~c cr~40 alC aICCIC illl1 lCLmu t~ l~ tNcll

tCLL CC+-l OlL ZI lt roIl elxt lL nL lgtll c- L==I c1lc Lo CGilLCMl ua4QJ 0 lt toIrr au co elf-C L

c c- ()=I cJc 4L al tlurc LIN ottlllw ardtCl (I1mL lgtJ OZI=Ir alo

I I

j

J

r I

10 t 01 L- 01

0

o ~J

tmiddott (4-x)T= ~

tff + cy = lJi I XI If ~jB = Bl I I I II i I urru tCt aalGI umNtU ULCtL tULCllL cmlULm CdlNlLh[CllLI GleNLlllII I

mni LINLl NU UffiL[lLIO cct urrCL GNUI C) UNO UULumLI tclITLCU II CLGLLdKLUi NO cl UUL GLUGlL UCLGLLdKIU LUU

I

i CNLGl NLClUL NU dLLL UlLLUU CULrnlL (AX)j

N) UKNl NU UumC[10 mt UUITLCU atlL uaLCLO UffiL(LO mt UGLUGlL E UNLli

( - tX-r)(txA + t9+(K+x)t1 =~

(tA- tX-r)(tAx + (x) + (K-x)e= c

urL CUffiGITU UUIm ITt Uh[[hdu LUGUUrlll C) Lmm NU UmltNlU UhWdU me ULmu mrnuu UGlrtiKdl UNrulU NU UGllLl ct NUl UNCLLU mt ct DGllUGl CCLU ULtLO NUL LmaL NU GlrdKLU UNrLrLU mt ULmu LUQCILL N) trl Lmu rLLUfLO N[tlrioU NrnL UhCUdU mtu UlCLtU tUKCU NlGGlLUtLU (Uuruu rnU06L CUI UULtLO lUU tUOGL UOllll[Gldl - N ) ITl N ~C tUL Uillmiddot cm cl uru~1 CUI UUl~Ln CllLrlO NU UOGllUGlLn t6L UITlGUO - mlC U ~ ~LKlL lCtUL LKlL tLlUL utitt hLll N CUD un LLKIO tmrJlU UUUUlLI cL mclu UULtLO ULKlL CLlUL udtt KILl LI

COLLO tLULlL lLGlNl uutdmLo ct UOGlll[QLO tlLr NU LmLUU CUI lUltLO

~ Guul tITLLU NlGGlIULlhLl tNUKCUU UDU LLGGLel Nr~lrLu

Ulul- meLm mcuu lUtUI1LO LmNIO tUffiuurn clb LffilUlU mULcl at LlO an a~ mtlm UNLta lffiNtllI lCNlU

GLl6 lHlL rLGlGLLI[l alal N I ZOO

[reul [LmLlLLl [lILl[l[l N iJ

tmiddott (4-x)T= ~

tff + cy = lJi I XI If ~jB = Bl I I I II i I urru tCt aalGI umNtU ULCtL tULCllL cmlULm CdlNlLh[CllLI GleNLlllII I

mni LINLl NU UffiL[lLIO cct urrCL GNUI C) UNO UULumLI tclITLCU II CLGLLdKLUi NO cl UUL GLUGlL UCLGLLdKIU LUU

I

i CNLGl NLClUL NU dLLL UlLLUU CULrnlL (AX)j

N) UKNl NU UumC[10 mt UUITLCU atlL uaLCLO UffiL(LO mt UGLUGlL E UNLli

( - tX-r)(txA + t9+(K+x)t1 =~

(tA- tX-r)(tAx + (x) + (K-x)e= c

urL CUffiGITU UUIm ITt Uh[[hdu LUGUUrlll C) Lmm NU UmltNlU UhWdU me ULmu mrnuu UGlrtiKdl UNrulU NU UGllLl ct NUl UNCLLU mt ct DGllUGl CCLU ULtLO NUL LmaL NU GlrdKLU UNrLrLU mt ULmu LUQCILL N) trl Lmu rLLUfLO N[tlrioU NrnL UhCUdU mtu UlCLtU tUKCU NlGGlLUtLU (Uuruu rnU06L CUI UULtLO lUU tUOGL UOllll[Gldl - N ) ITl N ~C tUL Uillmiddot cm cl uru~1 CUI UUl~Ln CllLrlO NU UOGllUGlLn t6L UITlGUO - mlC U ~ ~LKlL lCtUL LKlL tLlUL utitt hLll N CUD un LLKIO tmrJlU UUUUlLI cL mclu UULtLO ULKlL CLlUL udtt KILl LI

COLLO tLULlL lLGlNl uutdmLo ct UOGlll[QLO tlLr NU LmLUU CUI lUltLO

~ Guul tITLLU NlGGlIULlhLl tNUKCUU UDU LLGGLel Nr~lrLu

Ulul- meLm mcuu lUtUI1LO LmNIO tUffiuurn clb LffilUlU mULcl at LlO an a~ mtlm UNLta lffiNtllI lCNlU

GLl6 lHlL rLGlGLLI[l alal N I ZOO

[reul [LmLlLLl [lILl[l[l N iJ

1JUCAc a4-t l~lCll CZIllNlll ~~ ~~ ltla4LLNLll L~-tl l1~ 3UI L - 1m OllNCZ

pound) [lILtC tlaet1 tIl-t tLLLr~O NcQtClC1Ll~~C LNrJ~wC1Ll~tr axt ~Lt a4~ ~ NUll tlllNLC~LCl4l11

C ClNl 41- ZUl LL zNGQ C41LL cuna~

(tUl lt 1m) C dC-tL )llllCUI1LlNlll lrJCAlU CaLtLll NU LLTGUllLll tltll41-t La4t (0 0 ZUI ym) = tIl

I (I4l-tCd2 l~l(IC) C2Cl41LLNL CtlQQL

f tlC~ tlaCllltlLnl~U CClCLU NU 1Jrt4rAC 41~ lGlt4lLtC lN~llllil ~ LN middottlllc~u

tU1l lt-Sgt (CN41L lt-Sgt Lflt4L1il LUltlLLrtz4 1114 LOUlCCUNL 1+= IS) Z) CGLClCll40 -dUI tLlllU PI~rgdoE mrL~O aGGl wl urru IlCLll ~ lcd tlX lG~U

I UlllCl NU LNrLr~ lll~ LIAlU CC 414C lll~ crCAa (ClOGcd mL Nll LClcl4C) lENll NU IUGUUlU om clIti4Ac t4Cwf lttiL lt1 = I ltI- = I

r t(~U 4lL IUlr atL I lClcU 0 = 1 dlrG~nLLl lll4 CLlllU ~

cmiddot CNC N4llurrLU ~ulL ~XtLlll

N LtNL La1l NcI laxt

cm IIGG4-

LllltL NU Clal4XU lC41l4C Nllll UtQ~ 4lallL lurrlU lNf WtlU CClClGlC1lll NGQ llftN 4l U~lt

a

IltlL -u~LtIl dllULr Ll-tCAO LlllN40 4-lllUC2111 C llll~C4U O1l1d ~ ~LC ampt1 4 llllxl41 ~La l4U4LU tNltr

(C1llL t1 - poundooe L Le) GLlG 1IlL tLClGLlltl LL LLL ltl~

CUt CLalLIlLI ruiCQ N

JLKtllLi

NCllhW

l KuL CNLGl OCUU NU (lyUl LNL (J)W ([ClL UULULQ mULa ~c 1) (CLla LlLlucunu mm 1

t ill CLlU(mu UlLnWLU mC LlualCU CGLCliKLLl me == V

C UULN [dl1U Llmcu mc u1LCULliLll

N KLLL NU LCLcdcLCLU CUlm LlGNlLU

cUll m Or=I+= 111= JE[_= ill[= t1[0= D[

JpI+ tuE[+ lutll[+ ut-= wp 11

r+ IWE [+ fIutt1[-T rIUI_ = JP 1 -wp

lllLWLdu me llUC[lCU UULNLU aL l1ummmr llN dULQGllLLLO l1lN aut lm llNLlULCLGlLLuO ut

rUl(U UCIlCU m (lLllhO NdOLtlGlllLLO lNL(ULC1GllLLLO dKC ULLL mt C( UnLll(LO

tr iLCChdL m~ milL NLC~LoLLIlmiddot

mLL1TlU ULLKru 1CLll~

C cumo UaLLO m )DI l1lmU lLN CLOtlCLtLU - UOCLLL NU l1ucrLIO CNdU Ulcl N6ml cLUL

N UKNl Nl Ct1LLlU umcu m llLWLdl LUll C1KLtLl mcllt C6lrdKLll m InI

0lt1 IfULlU =i == (I)2

0gt I 0

CNmL llla I LlLN acLO me LlllU llGfLUL ll1ULKLC1 In1+ Ulmiddot [= J 0 lt [ lUGLCdKLl 2 Ulr1LU

iP(I)2 +Ul- = utp 1

lUmllNLl JULCU lmu m ClLLLC a N(clrLLO mcc NUl uua LLU CdKtUl l1lLW1dLl me l1lmU UllNLl au

pound il(1It1l me L(JJIl N(~LrLU

r lLNl mCGlUGLCllLll lOGd (UlCll ill Nct UliI QGlKLLrL UUlN ttl CNmL 0 +-ll co +- NO +-f)

C dcl Nl LUmLlNl lldLCCIU Nl tU CUKe mtL (OOtUUlltut)=nUl (LCdll C1

(UffittLU LmdLLLu) uumLlNU LaQGlL N all UCILCU l1UmUNlU ldlCmr NU Lrl(LQ nUl CmlL Ul11dc LLNL Cll LLN (JWICl

middot j11JJOJ iil~Ti 110 ilN 111 T1TiKll In17lJ mJ~jLm nN j 1

tt -rJCE W ilijiJ5Igt nJi317ll tv il7llTi n~ilnjJ U J it iV7ll PilJii ilK OZlgtO 1l1iO Kl 7il1 ilK roWI mjil a 7tv 0037 iiTK t37

n1TKm mZll 01) i37 (limit cycle) Ji innZl 7707J IT i1j1ZlJ Oji OK

1 JiP 0iUJiilN OJl1 Nl-1 C1~~OjiN Ol11U NE -1J nn7l CJllnil7i (4 l1tv7lil m~ Cv~ ntv-C Clil1 17J 1liN 71W (tt = EI) mCli

t ~YIt1 _+ shyrxe 0

8r =- x 0

~ + ~O(C~~) tvlO

xgto xlto

XgtD

Xlt 0

Olil1 ltv 71 1J mmzrt 1107gtKI7) Oll1 lill 7J 11 OtllC o~tvP OZljtv 11ru

V 011 nli17ZlJ Ol1Ol Oiil7jl 7J 0i1r1lN 0111 ltz1lJ K IN oUOOjiN Oji JjiZl OtOOjilKI Ollll Til ii1X gt JecII - OtliD-to1)m t7tlIC-i1ll111)I n07J1-l

110

T1iT37J MJ ME mOJKI I1171 Oil7l7ll 1 lIp 7tz1 iiji7ll1ii n1Ntvil 11K Ongt N h- JaEJ~p Ol07)tl1

Cl1l1 n017J~ 1111J 1- mw n1l1tz1 111O7J1K 11tz1 TJ Jail it7ll)I7tv 1~ J ho 70 ii3tpmO iP7lJ1 tv roilm nmpl iOO7lJ un 2-7 Itz1 OiOOjiN71

nJil7 ilmjl 7tz1 n17ltOl 737 iZl7 iU7tlN I7l 1

111lOK mljil17J 0iilU7 CKlli iI1 0K71 1

i1ntt1J

I

j

I I

I G~liLL t4 C5LCL ca~el( 1 lttr) CIL OltI L-ogtf I r C~J lLLC GlQClLC1 CLCL ll~ c~aClC~~ll aCCL ~l Lft~Ll Ipound~ ~L~ L~~Lcal i I )( Cll)(1 ~dlll tCl ~GtL~Ll Ll4 L~tC~d LLrl cd~Cl Lc~t~clt CGlrd~ m~ tI II I I

0= +[X] NULlI I I I X=+(X] tClL OltX

OWlL 1 L)( cJtr cl a LrCc1l~ o IdCl~a clr~~Cl al~ Itl~Llr~CI

+[lt1 + rIDr ] + LUI =tUI 11 bull+(11 + LUIroo] + lUI - = lUi 1I bull

aJr tLl~ L- iJlaquo 11

C tUUl Nl LCQC~~lU al~ td~LlL Ca1CL LL~l al~al NGalUL 4)(lClI~cLL 4CClL lL Ltn tQaL dl

LaQ~44Ll a~C C~ UalCL ClC-iLql X4OLL )(l (mdLl (aoq 3m Lm CClCGL Cl~-C UCGlC4u a~ ~l al ~GalL 4LClL i4 ~ClJcC moo 0 =lot(middot FLL ~U l4dr~ CCIralLL (IuI3m) UaCL ~L dr-dL crdLLLI a1CL

ogtX 0 = aB ~O ltx XJ = (x)~ ~ OgtX 0 = (X)IB Olt-x x =(X)IE

OcgDI4c4 91) CCIl c

IClaLl~L l((rLl

r dlt~ LL a~ tl~ ~LCLc~ rl~LLr~o NUl )(dClQ~LLL LmLL lMltQLLl ClL1)(LC 14 ~J

iCl -ll4~t1lllLUr LL4c~L~C LlllC 4-llLrczal eLL LalCL a~c1l4 Ler m 1pound4 al4Lal C)(L a1~4Ll LC)(ll

(c~~L C - pound00 L L) GLlG ttL llClGLtrL U w ru~

C1t CLalL1L tFCC1 ~

I G~liLL t4 C5LCL ca~el( 1 lttr) CIL OltI L-ogtf I r C~J lLLC GlQClLC1 CLCL ll~ c~aClC~~ll aCCL ~l Lft~Ll Ipound~ ~L~ L~~Lcal i I )( Cll)(1 ~dlll tCl ~GtL~Ll Ll4 L~tC~d LLrl cd~Cl Lc~t~clt CGlrd~ m~ tI II I I

0= +[X] NULlI I I I X=+(X] tClL OltX

OWlL 1 L)( cJtr cl a LrCc1l~ o IdCl~a clr~~Cl al~ Itl~Llr~CI

+[lt1 + rIDr ] + LUI =tUI 11 bull+(11 + LUIroo] + lUI - = lUi 1I bull

aJr tLl~ L- iJlaquo 11

C tUUl Nl LCQC~~lU al~ td~LlL Ca1CL LL~l al~al NGalUL 4)(lClI~cLL 4CClL lL Ltn tQaL dl

LaQ~44Ll a~C C~ UalCL ClC-iLql X4OLL )(l (mdLl (aoq 3m Lm CClCGL Cl~-C UCGlC4u a~ ~l al ~GalL 4LClL i4 ~ClJcC moo 0 =lot(middot FLL ~U l4dr~ CCIralLL (IuI3m) UaCL ~L dr-dL crdLLLI a1CL

ogtX 0 = aB ~O ltx XJ = (x)~ ~ OgtX 0 = (X)IB Olt-x x =(X)IE

OcgDI4c4 91) CCIl c

IClaLl~L l((rLl

r dlt~ LL a~ tl~ ~LCLc~ rl~LLr~o NUl )(dClQ~LLL LmLL lMltQLLl ClL1)(LC 14 ~J

iCl -ll4~t1lllLUr LL4c~L~C LlllC 4-llLrczal eLL LalCL a~c1l4 Ler m 1pound4 al4Lal C)(L a1~4Ll LC)(ll

(c~~L C - pound00 L L) GLlG ttL llClGLtrL U w ru~

C1t CLalL1L tFCC1 ~

291004 own ) 11)~ I mJtu)ln)~

ml1lV 1VI7WJ mNw 3 m) w

tl117 IM~1 MIUt~I1 nlluP 1 TJi nmgtT 2P O17l1)1I) (B) J)1i1 nil71li ml1gtT P 0lJljl0 (A) 77)l)1 nWJ

17 mm i17W OWP1 mtIj1JW (C) i1W1n nlV Otl

(05) 111W mJnO1J Ji =Jt 1 Ii = J7I(C)i1lU1l krt mJigtTiT W mJlt nIjJ1J1 7lOP71 P i1 1i)

1W~K~ m)S1~ _2 lPJIltTl1) JW tTl 11gt311) ll1m

x -x-sign(x)- y

y =-Ysign(x)+x (xgtO xltO) itTl1Ji1 Kltn JtTll ilOTil v 11K) 11UPJ1 11K n

yeO) =1 x(O)=O i1nnili1 Kln1l mnnln nK iKn (xy iiIVOJ 1iOl1 11K i)

(W1J711i17 J 7Jp 070 xy )

nl~1~ lTJ~I~~JK 3 I =1 3nJp K1t ODJ1 Cimw 11m C=l R=l 017 Jt17 Kn IV RC 7111J 11m K

nnot tTll1JTJ mn-r nK iKii1

(v(O)=O ) vV) = _t- 7Jpl I( rj1101J 11m Oim J17W l C1li1IV) VJT ni1n jl1l) mJl umtiJ l 3600

R 1 C W onl71 mi7 O)X 10

bull ~2 m1tJni11 17 01)1X01 Ci=1)2) C Ri OIjOi)1 011 OKn lVl 017 i1gt110 m1m l

co gt C Rj ~l gt 0 11=1 12 = 0 11m

(g =~ gtT) 1)1Wni1 nN JOi1 J 9I10J 0gt 11l1W 1m ngti110-r niil1J ml1 InJ OKR

MII~I-N m)S1~ 4 nnl11Ji1 ill1m

~= fv-w bull w= bmiddot (v- fW)

f-1 lt v lt1)= 2v-v3 iWKgt

fv gt1)=1 f(vlt-l)=-l

b=4 1 Olty i1JlI YW 0l1W Ogtil1 iny niiK)il miOl ill)iTil 1ii IlK1 mJpm 11K 1lWn K

y IV OllWil Oomnl OmJJ 1Jni nJWJ 11mpJ 11K tJwn 1 illtji1)lil iljOi)J mnl nltUi1 nmpJ nK i l

i1nXill

iUoUU)

elt DJlllJ nlnWlJ lnJTJ 2003 elt l]]lTJ

ITJn In ll1 lP1l9tJ1J llJn 91l9

TI1NJil nllNtDn llJ1Nn tDltD III Ull I1T I]) lJlilW mnW1 9TJ wnnwn7 I1~W1 I1nlnn nmrn rnl1tD -mTn

ll nD]U 1m lJ1JlTliJ 1

ilNnrnnn nN I1jln 1111) Iw nnJnnil INUU19 11 nnJD Irn ll1Jl11nJ dv

C-=-g (v-v )+A(v-v )2 +1dt L L L ut

llSn TIlT NlD Iexl 1 Jrn I1WTJ A lllllilrn (leak) n9Til TI1JIm gL lJj(n C 1rnNJ

i1l1SJ nN11rnnn nN JlnJ1ll9Nrn m1il N

dV shyC-=Av2 +]dt exr

V =v-vL - i~ lrrf =Iat -pound 1tDNJ

71n1JS ilm Iut lt 0 11J1) ilj7DJTn 1m nJtDn TI1Tlj7J lnn J oJ

91D lnT 1TJnIl v(t) m 1JI1 v(t) [(] 1N1n v(O) =Ot=O]1 lat gt 0 -ill 11m l

hdx(J--2 =arctan(b)-arctan(a) I1JUJNil 11m)1-- xa bull

J1[(] 1nn Inn lIlT nIlJ llJ1)J -co ID1lJ nN DlJJlj7 lTJnIl v [I] lmlt T

inl1~illllJ F rn mlil ( =F(Iexr) Iut ltD il~jI]19J lil J~iI Nmn n i

F(Icxt) =K~Iut - ItJo I cxt gt In I

o otherwise

nJ1lJnn Irn I1lJ1Jj7 lJ DlJJjlJ KJtb 1uno I II

T7991n nan 2 I I

nl99nil nN I1lTm kt 11lJTnPJJJl p I1ll TI991il n[(]l i1Jlm

LI 1J ~ul 111 =-IsiJ ~ (

j=1

(Sf = plusmn1 ) lNPJillillJil nllJ9 IUJ D)TiDlnn lJSmnil (sJ lWNJ

p

76908 liN [PJ~D nlnWl Dl1PJ npnJ 11072006 N 1111D

l~r(I) DlfJPJN mnln lnD 1P1l91lU llm n~nTl

nlNl1n n1NJn nliNUJn DJ1ND WlillD lJlJ

n1lJID lJJ1N ]TIJDn JUT

lI991n nml11 nN11 1

n~1n)~ n~in n~1 C1~) n2nn n~1n 1)) ci nm1JT P DlDJrnn ir991i1 nonJ bull lily nl1nl n~ O1~pn

Jnew - 2 J Hopfield a nllmUi1J iJ - ij

JW =0anllJnUnJ J~ew = JHoPfiBld

1] ij1-2a nllJnUnJ OltaltOS lUHD

(J)Dln lJlJl D~lnn nNl 1lrun nN 1J(J)n 1 DJ~I nllllJIn IJ(J) nClJ(J) Pmax nN 1J(J)n 2

co _xl _a1

1 1 shyS- aPr(-altX lt00)= e2a2dxSl ___ middot_middote2a2 1lClJNn Jlj7J lTDill1n] J2rca2 J2rc a _Q

nlU1J1N nllJ9 IW nlNPI nVDPI 2 nlUl1JlN n(J) 1w DlD~lnnn llln lJ~j7 Ill nj7n)lTn nJlnJ

odV1 = -Vl + J V2 +hI dt

dV2 o - -V +amiddotJmiddotVl +hl--- 2 I

dt - shy

Dlll1lj711 Dlll119n DIll1lJ Nl~nl111~ pNV (0)=0 i11nnnn NJn lUD Vet) nN lNtlJ (N nlJ9mi1 n~ltmll Dn~l1i1

i1JI~ nJW nT1i7J nJlllnl i1i1l1W nm 111 J 1 a Dltlp19n Ill NJni1 mn (J nTDl1JlNi1 1W 1w P91N Ill 1UlN i1T i1n nl~1D1N l1Jj7n DNJn l1NJ (1

lPWn J~j7 nN uwm nWln 1w nllmn n~j7J19 lUll W119n 11~PJ 1m a=l 11Jll (1

1 a1 11Jll nlNfllil i1nlN nN 11NWI1W9N DNi1 n111NilW 1nTJ ~

I

I

mUJ P~9 I11D ID n=Sct11 3

TIJ1DDil mlnJ

~=[(v)-w

w=bmiddot(v-yw)

[(-1ltvlt1)=tv-tv3 lUltD

-[(v gt1)=1 [(vlt-l)=-l

b = X 1 Olty 1UlJ

( 7rn nJ1m UJ1D 11JlJ mrn9il JnlDJ ilnlTil 1j7 mn n1lj771Jil n~ 1~~ C uc jl1l1C P~711E my 1m UJl[Uil UDlnnJ umJPJ 1Jlll nJrnil TIlTlj7J m~ nmn J

C7 1N mtD1~ j] U~il PI11 1111Nl ~I ~ i1J1 jlJil

nlJllJ mr~ IJm1 xJ 1~9Jnl mJ a+bx+ n~i7J19n mmmn n~ Ul1ljlJD rm~ lmNJ ml

il1j7119JilltlTIl9J TIl7n] w 7rn nJrnil TIlTlj7J nC 1lI1 1

QIF (=QuadraticIntegrate-and-Fire)

v(O)=vr v lt11

11 ilDJU I ill 11lD 4

il~llmDil 1 7lJ n7rn] (TIn nnmo 11m

C dv =A(v~)-vY +1 -10dt

ilnnilil cJn 1UlJ il~lrnDilllJl9 (a) (~ y dx f-2- =arctany) UJ lJJ 11TlJil oX +1

91U 1mJ lTJTID 11lTI9il J mlil (b) 7lnTIilllln91 mIll lDrnDJ (c)

nDljllJnc1JOJTI v(t+)=Vr resetlJ~mDrD vt)=Vr 1UJ~JUllJ 9U vr ~n () i I(f-1 curve) T-J3j1 U1T I

710 1m ilJl1jl nJJo~ I i11JJ I 11m I IUl IUD nDljllJil mmnn T~J p i ln nU1m nlTn 1 lUlU v=vrresetlTIRI nllnjl191 n91j1n 9U1] (Tr

7DlJ9n A 9lJOI TIlJlmTIn

i1n~i1]

I

mUJ P~9 I11D ID n=Sct11 3

TIJ1DDil mlnJ

~=[(v)-w

w=bmiddot(v-yw)

[(-1ltvlt1)=tv-tv3 lUltD

-[(v gt1)=1 [(vlt-l)=-l

b = X 1 Olty 1UlJ

( 7rn nJ1m UJ1D 11JlJ mrn9il JnlDJ ilnlTil 1j7 mn n1lj771Jil n~ 1~~ C uc jl1l1C P~711E my 1m UJl[Uil UDlnnJ umJPJ 1Jlll nJrnil TIlTlj7J m~ nmn J

C7 1N mtD1~ j] U~il PI11 1111Nl ~I ~ i1J1 jlJil

nlJllJ mr~ IJm1 xJ 1~9Jnl mJ a+bx+ n~i7J19n mmmn n~ Ul1ljlJD rm~ lmNJ ml

il1j7119JilltlTIl9J TIl7n] w 7rn nJrnil TIlTlj7J nC 1lI1 1

QIF (=QuadraticIntegrate-and-Fire)

v(O)=vr v lt11

11 ilDJU I ill 11lD 4

il~llmDil 1 7lJ n7rn] (TIn nnmo 11m

C dv =A(v~)-vY +1 -10dt

ilnnilil cJn 1UlJ il~lrnDilllJl9 (a) (~ y dx f-2- =arctany) UJ lJJ 11TlJil oX +1

91U 1mJ lTJTID 11lTI9il J mlil (b) 7lnTIilllln91 mIll lDrnDJ (c)

nDljllJnc1JOJTI v(t+)=Vr resetlJ~mDrD vt)=Vr 1UJ~JUllJ 9U vr ~n () i I(f-1 curve) T-J3j1 U1T I

710 1m ilJl1jl nJJo~ I i11JJ I 11m I IUl IUD nDljllJil mmnn T~J p i ln nU1m nlTn 1 lUlU v=vrresetlTIRI nllnjl191 n91j1n 9U1] (Tr

7DlJ9n A 9lJOI TIlJlmTIn

i1n~i1]

I

76908 N ClJ311UnU- oil r~l 0611 2006 - l j31~

oirn OltWJ~ n~11i11nll lpn90U 11m n~nn mKll ml11m 173lQ) tldrtv 717 JY

m17ili 1731 lOTii 1I1991i1 nWl 1

n~rn nUJli1lO (ilnW nnJnOilJ plusmn1) DJnHO qi nlJllJT P DDJ01O ii991i1 nWlJ D i1J1nJ n7W OlWj7il n~lOOW ilWln mIn Ol~l

ntDJ nllt9nilllnO OlnUil O1j70 lJmwn nil A lJH lWHJ J- =Aq J1Hopfldd

V n1J1llIl m ll~lOO WDln lJ1Jlll~lOO n~ltJPOil nH lJwn 1

OIJ~ nllllniltJ[I] nOJUl Pmax nH 1Jwn 2

J- 1 - _41 1 (j shyPr(-altXltoo)= r---- e2adx=1----e2a2 tlOlHilJllitJ1TlJiltln1

1Jru2 -a fii a

1011] P~9 tl1n 7D il~~ll 2

nJ1DO il i1J1nJ

~ = f(v)-w II

W= bmiddot(v-JW) f(-1ltvlt1)=tv-tv3 lW~J

f(vgtl)=l f(vlt -1)=-1

b =17(6 1 WOO lUll DmnnJ nJ[I]il nll1j71 1w mU~J Un1 nJWil nn1j71 nH uwn nU7j7tlm nH l1~N

t[l] D]lUlil

nlJ1U m1~ 7Jj7tl x J t9Jilt]n) a+bx+Yx il3j7119i1 mmmil nit DIDj7JO Unit W~J ml

mU~ nH1 H 1DOO nJWil nnw] nH w nl~il nJ1DOJ l~ 1 tll 1H1DJ b = 1 b=6 llJlJ Jl H O9DO nH nn9 1

11]) UP

tl~Ul

(wnL ~Ufim l e llLCh lJiL CIM C t llf~)

r fIILI OCOClU flU lCGILifl Jil M ClllfLCl Cl~1l C e fl1 fILL lUJiC UJiICO

0101 IlCG~UO 10101 OCltHJ)

[ [~- I j ]=w (NIl fILL ~UJiC CNIGJ IlGILfiI cul ~l01l 1ll1 OIlIlfilILfilIC lGI

LlCL tTl ILl UfillC OIlCO fiI~ lfI1f fiI~ lc(C1Lfl

Cl flUU c(lCiILIl l[WilIU CUUIC 01t rgtItgt 1- ~NUL C(CIILNI C flcl cL l iTtIL rraquo q l0l1 (CNIGI lICIU CfIlLU l1I1 lllC(l I~~N UlfillCC) Ill lICIU tnl

C IILl OCC(l l1ltl NU CLILlU luuIL lNGfilL1 iTtIL 1l0GL flLCC fiI~

c(li c~ lcLILJU Cl1J lCULU IlUflGOU UtnCl Ll NU ffLC lGlcLl IflU tTLC lCtlLU lLNJiICl C 0 IC T+ CIlI c1 IlIANI

N IILI NU lCI~i~ICIU Ltu eLI huL NU lGllICICl NIl AILL ~UlIL fllUI CNIGI C(lN

0lt q [-=(T-)I) T= (1 lt11)

z z CNfilL poundd~+sl1 pound_ =(1)11gt [-)1

(M( -11) q =6t 6t -(It) =11

LCCI GLOGClU GfillCl NfilL 1lLC~ NU (1)li Cl~Cl ICL~L (GlCl = ~) CNJiL (O)lin (O)ib(l)rt lilfl (O)H=(I)n )

t fftILJ 1lJiUCl Clll all [UILltIL fll J CNfilL Clld 1l01O I NeUC) cUNd CI

ClOCLI cAL 1ll[[lHC lWILCU ITCJL J iClfI

NGUU NU lllflLCU (L111 ~lfIlL ClIXIUCChll GI~flLl 1llU~IU Wi1Cl on-li=rt )

fftIL [r~ ~]=N CflJiL U]=(O)gtgt [~]=~ (on -11) N() f =11 CNJiL oli llfll1 lCOIO filL lC LhL I IlGICll J olN~LIl n clCU ffL L

lNICLIOlU Ul11 Clct ICtLIJ fll ILl tILIJ Ult ~llflLCl (CIILIIlILl~ClIL) lLCaLl fiI~ lft lL ClICl C(ffLCU fill filUI NIClIOIl tLltlC NiOClClILl INClCClILU CXJiL lltIIL CI Jil

euro UffLCU 1ItNUU GLOGCUrI ltlfilL

1 mJlJO 7m Ill 3 R nnuni11 C n71Jji nllltJil nplumnn nlJ1Jnil 7lJJ (JOllt9) J~ Nn 11m

I(t) lltlil jilnlln D1Ti11 0 lltlil NnJ n7nnnil nnllilm 11m 111lm 7m nSjil19J NnJ nnlln lilll llt

OlllJ9 F 11l lmlltJ lltn7 jilnllil Q Il11J llJtlll Iw illl~G N1il Nn7 jilnlln Olmm 11m ilHDJ

let) = LQ 5(t - tj) nllnllt DIIOJ

J-(J

r j =f lWNJ

cmiddoto NlilllltlPNiltmnN)t 0 $ t $ t lWNJ fI J(t)5(t-7)dt = J(t) nUjill lt5 nSjiJ191 o

vet) 1ilD J ilJllil

1lOn 7l11 nS1~tlJm nnjO lTD l7nil7 nJ lmn 1

qn+l_lLqi = 2 k~O q-l

1nm Nln t) 0 $ tr lt Yr- m1J 7nDi7nn DJ1lil 190nn Nm n lWNJ t = tr +t lJnlJ 3

(t 1Dll11mm 0719il TNn FRCtrnQ im 11nJ1nl vet) nN lN~l 4

ONJn nl1JU l1l)Jn nNll TiJ J

lmN lilU lJ1JjI Dll 1m illjill ill illjlll l1mn (e l+e W llJT) RCraquo Yr- a 1011

RC laquoYr- b (nJ t ilT O~J) 111 n lWNJ ab Oljlll C

llJtlll njilm 7J lnN l1l1 )91 Ill nnllil iPil nll c J 9lJDJ Dlj111n 113lJ t (tr = Otr = t- e)

ilpml nJ1Dllil ilJlm

X=-x + y - ax(X2 + y2) (l 2)y=-x-y-ay X +y

a 1tlDl9n Iw O)lWil OJ1lJil11JlJ nJ1lJllillW lJWllil nN 1~0 N (x y) 11W0J nOlTn lljf nN nlJN 191NJ llNn J

llNn illlD ilD1 nspll9Jil1tl1l19 NlilO P ON 1T nJ1lJOJ ilSjfl19J mw mm 1

ilSjl119Jilltl1l19J mlnJ lJWOil OP11 nN 91l191NJ (r B) mlNI19 nltlNr111NljiJ WlDWJ 1TlJillllJ1n Il]lll

rr=xX+ yY r=~x2 + y2

yx-iy TNl (y)e= - e= arctan -

ilnl~nJ

f 0(

Imiddot

I

i I

76908 liN OJgU nlnWl lJl1pJ npnJ

11072006 N iUln

tlaJ DlaJJN mnm lnlJ lPl19tl1l llJn mnTJI

nl~llil

nlNJil nlNtDil JJJ1NTJ 1D1W I]) 1JD

n1lJID ])J1N lnJTJn 1TJT

T799ln npoundIll III il~~l

rl~)JlI nll1n l1l1 O)~i) l1llttn nlln 1J r l1i)nJT P IPUJ1llD T799ln n[l]1J reg )11)1 rum) nlI o)lIpn

J ~III =2 J opjitld a nnmOilJ Y Y

Jew = 0 a nllJnUilJ

J~ew = JopjiddY J1-2a nllJnUilJ

OltaltOS 1[1]NJ [I]ll1illJlJ1 ll~lDn nNl I1Puil nN u[I]n 1

DmiddotJ~ nlJllJTil 7J[I] n1lJ[I] Pmax nN UDn 2

co __ xl _a1

1 f2 (]1 2lPr -( a lt X lt 00) = e ~C dx == 1---middot_ e cr 711lJNil Jllj7J lroil7 In) J21L(]2 amp_Q a

nTU1Jl~ nllJ9 7pound1] nl~pPI i1lTJPT 2 npUl7J1N n[l] 7[1] Dll~1Dnil 1il J~j7 7D ilj7nplil illlnJ

dV1 = -VI +J Vi +hlo

dt

odV2 =-V2 +umiddotJmiddotVj +h2 dt

O1ltJjill O[I]119n O1t)J Nl~DI 111~ n~ V (0)=0 illnmln NJn 11JU Vet) nN mrn (N nJ9lnil il~11lnl1 On~Uil

mJ~ nJ[I] nT1j(J l1J1llnl nnn[l] nm 7U J 1 u O11111l9il Ill Nmn lnO (J ml0llJ1Nn n[l] 1[1] 191N Ill lDlN ilT no mp~IU1N l1Jiln ONJn llNJ (1

ll[I]n J~j7 nN u[I]m nalln 1[1] il2l1Nn n~j7J19 lUU Wl19D mJ 1Jn u=l llJU (T

a=l lUll nlNwn ilnlN nNI1NW7 1D9N ONil il2lmil 1[1] 1mJ

76908 liN OJgU nlnWl lJl1pJ npnJ

11072006 N iUln

tlaJ DlaJJN mnm lnlJ lPl19tl1l llJn mnTJI

nl~llil

nlNJil nlNtDil JJJ1NTJ 1D1W I]) 1JD

n1lJID ])J1N lnJTJn 1TJT

T799ln npoundIll III il~~l

rl~)JlI nll1n l1l1 O)~i) l1llttn nlln 1J r l1i)nJT P IPUJ1llD T799ln n[l]1J reg )11)1 rum) nlI o)lIpn

J ~III =2 J opjitld a nnmOilJ Y Y

Jew = 0 a nllJnUilJ

J~ew = JopjiddY J1-2a nllJnUilJ

OltaltOS 1[1]NJ [I]ll1illJlJ1 ll~lDn nNl I1Puil nN u[I]n 1

DmiddotJ~ nlJllJTil 7J[I] n1lJ[I] Pmax nN UDn 2

co __ xl _a1

1 f2 (]1 2lPr -( a lt X lt 00) = e ~C dx == 1---middot_ e cr 711lJNil Jllj7J lroil7 In) J21L(]2 amp_Q a

nTU1Jl~ nllJ9 7pound1] nl~pPI i1lTJPT 2 npUl7J1N n[l] 7[1] Dll~1Dnil 1il J~j7 7D ilj7nplil illlnJ

dV1 = -VI +J Vi +hlo

dt

odV2 =-V2 +umiddotJmiddotVj +h2 dt

O1ltJjill O[I]119n O1t)J Nl~DI 111~ n~ V (0)=0 illnmln NJn 11JU Vet) nN mrn (N nJ9lnil il~11lnl1 On~Uil

mJ~ nJ[I] nT1j(J l1J1llnl nnn[l] nm 7U J 1 u O11111l9il Ill Nmn lnO (J ml0llJ1Nn n[l] 1[1] 191N Ill lDlN ilT no mp~IU1N l1Jiln ONJn llNJ (1

ll[I]n J~j7 nN u[I]m nalln 1[1] il2l1Nn n~j7J19 lUU Wl19D mJ 1Jn u=l llJU (T

a=l lUll nlNwn ilnlN nNI1NW7 1D9N ONil il2lmil 1[1] 1mJ

76908 nl( DfJ~lJ 711711l1l OlIj7J ill1nJ 250707 I ilJlll 1J7IU 017IU11 illilil iTJ iJIIgtOll llJn ilYlO

nlKlil nI7Kllil Jl tKO 1I1711 7J (lV

I~n onl1JIU Plril

110tj70j 11nJ1l ill ilj7ru j 1

n71119 l1gtiJOil plusmn1 Ogtillil 111 7lj17 71gt inN 7gt 812 OI11N l1U OlJ l1gtilJO iJ1n)

I TIl nlIU nlilnOil1 Olil1lil inl Oinll 17IU 7gt1 IT ssf 7IU ilj1Oliil nnl1 OIj10i 10T1

11111 OillUYl II Ogtgtln ilJYln 1IIilnOil7 Olltl1nl

1U1gt P(plusmnlt+L1t)=I(lplusmn(S)) Ilil 011 lOll i nl illlJ llJlln 1IIi1110n

10=[ In(Ji)] J=[ 0 In(2)] (S)=ta h(P[plusmnJ S+h])l -In (3) In (2) 0 n -=1 11 J I

r n-Itanh (In (fn))=--J 1U17 1ll 1U O11IUnil 111n1)lil~71

n+ p= lco 1llJ ON1n illJOil 1gt0 ilnllllUn 1lt

p(-lJ-+llJ) i p(II-+-II) n

O~Yln nJ111lt 7tJ 1lIlllltil 11llIltJn E(S)=-~ LJIJSSj-Lh~Sj J IIm1 I j

1IIlnmil gt7 I1Jn ( Js+ 1 Illlog 6 Ill) 10 1 Ol ilUgtll 1gt00 llngt7 li~ K1)

P=] iDlJ 1~Yl 7gtl ~Ylil7 11gt1lI11il 1J I)on illl Ill~1I1 - V -lE(s) e-l 5 (s)Z-Le P(s)=-zshy

il1lJ Inlgtllil ITllOil rlij1lJ Oj11111 I [)llJOll OillJlln lJ illlJ ) 1J119Yl1IKiill P=l

11m1Il ilXll01 KllnT m7Kj70 Il iliilil 2 i 1J 1IilltlnYl OiYlIiYl OJI1I) IlJ 7tJ ilj1lllin

dV 2

T-1=L Wi Vj+h iE 12dt I=

Wj=-(I+euro) WI2=W~I=-(1-c) hl=2 hl=4 T=2 iJllgt

7j7IUYl IItJ7 ilJJlil7 l911n IYlTil InYl 7j1JYl 1IIU1 V lilYl E=OOl il1lJ1

ilYl i1ll inlllYl I1llJ 5 V lilYl 07 h 07j1n nll OlJll 7j7JYl IIJ 1~Yl11 OYlYlJil OIOj7l1ilYl inK 7gt7 ii9l1 on lll1il7 111) O)I11ItJI11 ilT inl ilij7

euro=OOO 1 tJKgt 2 I 1 7J IllJ 1

lilYl 1J7j7il 111 Oj770Yl t=1000 Inn V(t=JOOO) lilYl c=OE(O)=O illlJi

1tJil O7j7illl 11i)[T l1nlJYlil ilYl 171lt lJlln7 l91lln IYlTil Inlll 7j7IUYl 1II1 V

l[(l+C) (I-C)]Oil 2 (I-c) (l+e) il~ilmil 1IU OIlYlJil OiIUj7HilI OYlYlJiI OgtilJil iliJil

(IO(I-l)) I Ie) middotmiddotmiddotllYlil

(IlrICL ~UtiIt l If lpoundlLCh NtiL tlhl1 t ~111~) I IIILI OCOClU ilLC lt1GIuIl til M tilI1LCLC CU~ILC t If iIIlILL lUtit Utrllt1J

001 IlCG~LCIJ 101l1 ocmlJ)

[ttl- j]=w (iIIlILL lUtrlt CNIGI ilGILti culllolpoundl illJ 001 ltiILtrI1J lGI

lLtL 11~ l Utrllt OiltlJ til l1111 trI~ lOClLoll c~ NUU illCclllU l(ilNIU tLCUIIJ 0 1 gtgt 1- lNUL aclllNI c NcI cL

l I1tIL Iraquoq lOIpoundl1 (tNIGI NCILC tl1lLU poundl1I llLIll 1llN UtrlltllJ) 0l1 lltILC til

t eL lUtrlt NLC l tt liLCl (t1 cILl ltrICI) Uiit1 NLC CcILU lliill tIltllpoundllmc

Ol1 cl lCllILIU tlC lC1lLLC OIlMGOU Utrlt1 u Mil I1LC lGICcll lilll IILC lCtlLU lLNtnICl t 0 It T+ bull Ctli cJ 01~1

N 1iIIU NIllalt~CILC bull LW CL llIIL MLC lGIlCIC NI1iILL lUtIL NIIlI tNIGI OlN OltAq

I - =(r - gt)1 I = (I lt )1

z z CMtrlL ( 11 -S+sl1 pound_ =(1)gt 1-)1

(M1 -11)q =M M - (11) =11

Lta GLOGClUI GrnlCl NIiIL oltl Nil (J)n ctlO I ICLll (GlCl = ~) CNtiL (o)nlgtin (O)ti=(ll)d JIN (o)n=(I1)n )

I1tILJ llJ7IUCl OIlJ Ill CLCJ llIL I1lJ CNiiL UIl il011l1J I Neuel OIlNJ CI

tlOt U CIl OUCltU lOI1LCU I1tIL J ttut

NGULI NU lIlI1LCU (L1 lltlL tpoundlINILLtCChIU GI~NLIU 1llUlU llJ7IUCl on -n=d )

I1tIL [I~ ~l=JlT CNtrlL U]=(o)n [~]=17 (on-71) JlT(1) 1=i CNtiL 071 l1~UIltOO til poundllt lL IlGICtll J OtNlLu Ii (ueu 11l l

lNIClIOIU Ulh old IC1LO 11l l 1ILO Ullt lIlI1LCU (CItLltlIlIlOIL)middot llCoil til poundllt lL tllICl ill1LCU fill rnu NIClIOIU C]L1CC NlOOOILU INCltOILoU CMiiL lltlIl tlt trlU I

pound tlltLCl[ JtNtlU GLOGOLJI lt(rnL

J

131207 ~ ill1Tl 1lt Ol11l nntl~ nlT3 i2li~Utl 111n n~iTl

Ov ClV1~ n~iln iny

nlI~ 4 l 1lttf 3 1I llll USl)1n 1 nI1lt~

1 Y ilJl11J DlIVpn l1~ll)1J I ~~iIlJ DJmm l11Jlln P oYJlJlD l1nlt 1)Sl1n l1Vl1

J mnOJ Ul~m llrln

J olIVp 111) 1T11lt 17~ht DJnltO 111Jllgtr 2P oYJmrl nJIV TISlSl1n l1Vl1

J InlJ11O

1 bull -~ 2tl _ e2tlPr- a lt X lt eo ) Je dx -= 1- -- - llJJltil 111PJ ltYi1 111)

-h1ampti 1 S-a a

imiddot~lUl1lt - 2 1900 nllto R l1nUl1m C l111P 111rlt1il 11101Onil l1lJ1Jl1il YJ (JOrltSl) 1~Y lt11 11m

let) lt1n plnOil Dlrlll O(Iil rlt111 l1nT1ilil nl1Dmv 11m CJ 1OJ) lDril IV il~PJ1SlJ rltT11 nl11Jil lilDl

F -rD 191rlt1 rltn jnnDil Q I1U lYlJD gt10 illl1 lt1i1 fltn plnDil [)lrmv lln) 2

5 11~PJ1Sl1 r J = f lOfltJ 1() =I Qmiddot6 t - r J) l1nn~ DD1 ilJIV1 ODY9 jaO

I

0 flt1iI nmJfltil l1lnfltl 0 S r s t llOfltJ J(t)5 (t- r )dt (f) l1DPD o

vet) 1ilO3 ilJllil

1JOil 1D il~IlJJrlt lTD t)mil OJ 111m 1 t qi qnH - 1 2 t o q- 1

n IV lJ DOPOil YJlJilISlODn lltlil n IIVltJ t=tru+T=tru+ F 1JDO3

bull t lV lnnrltil lill1 TlYIV 1Dril flt1iI tm rltlIr O=trult i Qntr bull RC F IV onJlDJ v(t T1flt1rltlJ14

oltJil T1TlUJ mJil illtlJ ~J5 (e l = 1+ E II llJr) RCraquo ~a

RClaquo YFb ilD m illpD1 Cngt t m D~YJ) n) n llltJ ab DlpDc

jYI)1J l1plm J 111lt Im J9 -rD nnDil ilil

PlTJ Oflt illPD JJ v ml1lV ~J (t Ot =t- pound) (111 lntlt lltOl Y~lDJJil Dlm) 1111il l1~nDJ lSlgt 1Yl)1J

IV lgt c nlVln T1IVlllU lollVpn T1l~llJO nltY1

23 nllJT10il1 J=J 113 l1nJT10nJ J=J

Pnll= l1rltllVYln Y1ll YflOrl mlt JOil 11rlt lllVn ol~ A IV l1Ullnn gtJ1 OJ~ B IV l1nngtril J2

O1~ B lV1 A IV ntJllJrIl gtJ3 1 (j a~

-

I I

II

II

-

n~1tJtJ~iN1 n~11tJ~l~n)~N CI~211~ n~1J~N ~v ni~t)N2~f - 3 1poundraquo0 nraquotv j) Y O1NnO n1ln)N nnN) n1)t)PN nnN 0)1) n)t))7)lN l1W W 1m l~P

n)ON)in mN))WOn

TaVa =-Va +ga(ha) a=EI

~=~~-~~+~

~=-~~+~~+~

nN ha nt))gtlNnw 10ln Y)lP nN Ta gt 0 rrgtt)m~Jwm l~P nN 1NllO Va 1WNgt

nt))raquoNn W p-ln n~p))1 nN ga ( X) 1 nt))7)lN pn

=1nml

gE(X) = ~[xt TE = lJEE = 4JEI = 2h1 = 1

1 0g(X) = XT = -JI = OJE = 2h = I ext3

I ext J n~p)lIgt 1ml~ nN 1Pil) ngt1Yrm w mwn mjlp) nN N~O N

I ext w Ogt1Y111yn l1N )~O) Hopf n)~p1lll 110P l1Nln 11gt1YYllW lN1n l

n~p11lln milpll1ilPll

ilYl1ln np l1N 1Nll) 1)~t))Nn 1nNl ml)p~mn raquo))P l1N l1~ 1

I ext W n)~pm)gt l1N 1Ylll 11gt1YYln ll)lnlllnW ntNln 11011Nj l1N 1Nll j

bull~I)1 rltlrI m 1i~~ - 4 c) mc~

11tV1l m17~1 l~t7) 1l ~~ 1lT111ll111l 1)Dnl Ci11tJ Hopfield 11W1l mil CtJ~1 (Sj =plusmnl Nll 11111 tii tJJi1tJ111171tJtJ1 ltS tiiNl) ltSl

l1ljil1tJ K1 Il 1N1 1N1 CtltJ~1 TJJ ljitJJi1 l1N l117lji1 mN1tiitJ1 l1ll1tJ 1tJ N- tl1~tJ11TNtJl11p31 C1il 111111NT1 l1l31tJ1 CN1 bull tlOtJ1 l1N1TJJtJtJ (cji171 Cltii1) mil = (ml m 2 0 0) lltJ1 to 1tJTl mnmll111l1R m17l1i1 mtJli1 mN1tiitJ111N lP l

(ml gtm2) 2

(JIn 1itii lNtii 1nt1) PTJJtJ 1tOl OlN 117 m -TJJ N1 1 lIn~~lIl

ltG

h

N lllllll nlnlYl Inl))

2008 A ilJI))

i]11I9lJIA llln 9119

m~)il m~illil lJ)l~U illlill lJ lllJ OT1 lJ 1JlilEll nllJ~Elll crrj UmnEllil lJ~Ull OTUnil nllJUl illlUl-1mil

[Oln-n~ nTJ~ 1

nN 0I91J ~t l11JT nPJJn p mlJ)E)llJ OlNJ) 0J11lJ N Ul nElll)

TIE))Uil Pma- li1U a ml)nUil) co) 1991i1 lllJ) Jij 0~9PUil DlCIJj7il Olj7U Jill) llT m)~ 1il nPJJnil Jm

c a N c -1 )

n711U iF~11nJ1Rl1nT n1ljlo lJ iln9il 2

il~)il iljlUPlil TlJ n1~mu DTllJs IPJlllJ ][l] Ul iljrDJTil

r df = I Wij~Tf h (ij = 12)

l~mJ

~Vii=-(l+g) W12=W21=-(l-c) h1 h2= 7-2

amp=00111JlJ R j7UlU llEll illJm P91~il lUTil 1I1U j7EllU 11Ul) V 1I1U

1l1TJ 1I1U 1-0 - Elj7il nN OJWD IjlWU I11ill7 illJm nJ1lJUil lm~J i1T 111~ illj7 ilU

amp=000J 11JlJ mNUlil 1mN 7lJ 1JlJ J amp=0 1m illj7D] 111J J

11m] V1I1n Elj7il nN Oj71UD (=1000 1m) l1000 1m) V lnn lRlJml Pl91Nil HUil mm Ijlmn

il~l1lUil m [pn~lJil 0~lmjl1il1 On~lJil 0J1lJil lID nllJil

lr(l+8) (I-o)]ilDNnil] (11) (t-1) -1 (ls) Oil - 2L(1-e) (1+8)

xp(x)t(gUJ =(xqso) Ulshy

P

l UCL LKLCLU me mCL LUKLQ LNeu r UKNL NU UCILL me ur LNU LNCLrLL nOCL LWKLQ LN(L Co 0 gil UKCL rnllL urn le C LLNL rnCICLL pound1 UQ6Ll rue LUKCLQ (Oourm) L-(OOUImUI) LQ

N uul LUmLLNlU UllCULU NU UKCL mLL~ LamdeL

CUL[l ere LlL UmLrLL LLllGm U (eCLLLLl) me LITIU ULGGL(l CIQ d lCUCLU eN ULGldl (dnL6J

(cunl lUdillC IJ ( IJcilCl NI7IL C1Jtr C ( l((rl)

r Aull OCUCll NLC IJCGILll11 I7IIM CwtlCLC Cllllll C I( Nil JlllIUfiC UdjICQ

oal aCGllla loal oClaa)

[~~- 1~-]=fY (Nil ILL lUtnC CNIGI aGlI7I (lIllOllaIJI OalltnILtna lG

Iltl (l L lJtnlC oam tnl ltttt fl laalJIJ

cl NULC WCllILlll IJcaNlll ClUIQ 0 I gt11gt 1- lNUl UcilDH c Nci cl

IJ tttll [raquoq l0L1 (CNIGI NICIL nllLl Illh lllal 1lIN Ul7I1tO) al lICILC tnl

all cl l(lIlJU tIJO IJnllll allNGOl

Ufiit1 III NLC trU lGltllAIl INLC ttlC ltUlll IJlNfiiICl t 0 rc I Cal cl aANI

N Jull Nll lcllillIC1LC bull Ull elI lAlIlll lGIIC1Cl NIl AllL IUlll N1LCI CNIGI wx Oltf( q

r - = rl - gtt T=Illtl)

CXfl 1gtgt [-)

(mti -tl) I =11

xp(x)t(gUJ =(xqso) Ulshy

P

l UCL LKLCLU me mCL LUKLQ LNeu r UKNL NU UCILL me ur LNU LNCLrLL nOCL LWKLQ LN(L Co 0 gil UKCL rnllL urn le C LLNL rnCICLL pound1 UQ6Ll rue LUKCLQ (Oourm) L-(OOUImUI) LQ

N uul LUmLLNlU UllCULU NU UKCL mLL~ LamdeL

CUL[l ere LlL UmLrLL LLllGm U (eCLLLLl) me LITIU ULGGL(l CIQ d lCUCLU eN ULGldl (dnL6J

(cunl lUdillC IJ ( IJcilCl NI7IL C1Jtr C ( l((rl)

r Aull OCUCll NLC IJCGILll11 I7IIM CwtlCLC Cllllll C I( Nil JlllIUfiC UdjICQ

oal aCGllla loal oClaa)

[~~- 1~-]=fY (Nil ILL lUtnC CNIGI aGlI7I (lIllOllaIJI OalltnILtna lG

Iltl (l L lJtnlC oam tnl ltttt fl laalJIJ

cl NULC WCllILlll IJcaNlll ClUIQ 0 I gt11gt 1- lNUl UcilDH c Nci cl

IJ tttll [raquoq l0L1 (CNIGI NICIL nllLl Illh lllal 1lIN Ul7I1tO) al lICILC tnl

all cl l(lIlJU tIJO IJnllll allNGOl

Ufiit1 III NLC trU lGltllAIl INLC ttlC ltUlll IJlNfiiICl t 0 rc I Cal cl aANI

N Jull Nll lcllillIC1LC bull Ull elI lAlIlll lGIIC1Cl NIl AllL IUlll N1LCI CNIGI wx Oltf( q

r - = rl - gtt T=Illtl)

CXfl 1gtgt [-)

(mti -tl) I =11