离散混沌系统的Matlab仿真

Matlab1,2(1.,230039;2.,230061):Matlab,Matlab.,,.,.:;Matlab;:TP273:A:1673-162X(2006)04-0037-04,,.,,.,[1].Matlab,,.Matlab-,LorenzRosslerVanderpolDuffing.Matlab,.MatlabMathWork,,.MatlabSimulink[2,3]Windows,.Matlab,Matlab,,,,,.Matlab,,Matlab.,.11.1LogisticLogistic,,,,,.,,[1,2].Lo2gisticx(n+1)=x(n)(1-x(n))(1)3.574,,x1,,,.editLogistic.m,debug,1.:2006-06-28:2006-09-30:(2006KJ249B)(2005JQ11153).:(1970),,,,.()JournalofHefeiUniversity(NaturalSciences)200612164Dec.2006Vol.16No.4:functionf=logistic;%i=1;=4;f(1)=0.3;%whilei100%100f(i+1)=3f(i)3(1-f(i));i=i+1;plot(f)end1Logistic1.2[4],x(n+1)=ay(n)-dy2(n)y(n+1)=-bx(n)+cy(n).(2),,hopf,,;(2)Lyapunov,a,.1.35a1.46,Lyapunov,;a1.46,Lyapunov,.editcircuit_chaotic.m,debug,2.:function[f,g]=circuit_chaotic;i=1;a=1.45;b=1.1;c=0.1;d=0.2;%f(1)=1.1832;%g(1)=0.5916;whilei1000%500f(i+1)=a3g(i)-d3(g(i))^2;g(i+1)=(-b)3f(i)+c3g(i);i=i+1;plot(g,’b’);holdon;plot(f,’r’);end1.3,.83()16[5]:x(n+1)=rx(n)(1-a1x(n)-a2x(n-1)-a3x(n-2)),(3)2,x(n)[0,1],n;r0,.,.,.,,.,.,y1(n)=x(n)y2(n)=x(n-1)y3(n)=x(n-2),(4)y1(n+1)=ry1(n)(1-a1y1(n)-a2y2(n)-a3y3(n))y2(n+1)=y1(n)y3(n+1)=y2(n).(5)editbiology_chaotic.m,debug,3.:function[f,g,h]=biology_chaotic;%i=1;r=2.7,a1=1,a2=1,a3=1;%f(1)=0.2;%g(1)=0.1;h(1)=0.1whilei100%500f(i+1)=r3f(i)3(1-a13f(i)-a23g(i)-a33h(i));g(i+1)=f(i);h(i+1)=g(i);i=i+1;plot(f,’r’);holdon;plot(g,’b’);holdonplot(h,’g’);end934,:Matlab32,Matlab,.,.,..:[1].[M].:,1992:24225.[2].[M].:,1993:122.[3].MATLABSIMULINK[M].:,1997.[4].[M].:,1999.[5]MirnalRM.Biologicalpopulationswithnonoverlappinggenerations:stablepoints,stablecyclesandchaos[J].Science,1974,186:6452647.[:]SimulatingChaoticDiscrete2timeSystemwithMatlabZHUYe2ming1,QIAOZong2min2(1.EditorialDepartmentJournal,AnhuiUniversity,Hefei230039;2.DepartmentofMathematics,AnhuiInstituteofEducation,Hefei230061,China)Abstract:Thispaperpresentsamethodtosimulatechaoticdiscrete2timesystemwithMatlab.Atthesametime,aprogramofsimulinkchaoticdelayeddiscrete2timesystemisgiven.Thenforhigherorderchaoticdiscrete-timesystem,theapproachdiscussedcanbedegradedtooneorderdifferenceequa2tion.Asaresult,chaoticdiscrete2timesystemcanbeeasilysolvedbyMatlab.Fromsimulating,there2sultgainedherewillbenefittothesynchronizationandcontrolofchaos.Keywords:chaoticdiscrete2timesystem;Matlabprogram;simulate04()16