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1、matlab编写的Lyapunov指数计算程序已有2406次阅读2009-12-2908:37
2、个人分类:其它
3、系统分类:科普集锦
4、关键词:李雅普诺夫指数一、计算连续方程Lyapunov指数的程序其中给出了两个例子：计算Rossler吸引子的Lyapunov指数计算超混沌Rossler吸引子的Lyapunov指数http://www.pudn.com/downloads39/sourcecode/math/detail132231.html二、recnstitution重构相空间，在非线性系统分析中有重要的作用function[Texp,Lexp]=lyapunov(n,tst
5、art,stept,tend,ystart,ioutp);globalDS;globalP;globalcalculation_progressfirst_call;globaldriver_window;globalTRJ_buferTime_buferbufer_i;%%LyapunovexponentcalcullationforODE-system.%%Thealogrithmemployedinthism-filefordeterminingLyapunov%exponentswasproposedin%%A.Wolf,J.B.Swift,H.L.Swinney,an
6、dJ.A.Vastano,%"DeterminingLyapunovExponentsfromaTimeSeries,"PhysicaD,%Vol.16,pp.285-317,1985.%%ForintegratingODEsystemcanbeusedanyMATLABODE-suitemethods.%ThisfunctionisapartofMATDSprogram-toolboxfordynamicalsysteminvestigation%See:http://www.math.rsu.ru/mexmat/kvm/matds/%%Inputparameters:%n-
7、numberofequation%rhs_ext_fcn-handleoffunctionwithrighthandsideofextendedODE-system.%ThisfunctionmustincludeRHSofODE-systemcoupledwith%variationalequation(nitemsoflinearizedsystems,seeExample).%fcn_integrator-handleofODEintegratorfunction,forexample:@ode45%tstart-startvaluesofindependentvalue
8、(timet)%stept-stepont-variableforGram-Schmidtrenormalizationprocedure.%tend-finishvalueoftime%ystart-startpointoftrajectoryofODEsystem.%ioutp-stepofprinttoMATLABmainwindow.ioutp==0-noprint,%ifioutp>0theneachioutp-thpointwillbeprint.%%Outputparameters:%Texp-timevalues%Lexp-Lyapunovexponentsto
9、eachtimevalue.%%UsershavetowritetheirownODEfunctionsfortheirspecified%systemsandusehandleofthisfunctionasrhs_ext_fcn-parameter.%%Example.Lorenzsystem:%dx/dt=sigma*(y-x)=f1%dy/dt=r*x-y-x*z=f2%dz/dt=x*y-b*z=f3%%TheJacobianofsystem:%
10、-sigmasigma0
11、%J=
12、r-z-1-x
13、%
14、yx-b
15、%%Then,thevariationalequation
16、hasaform:%%F=J*Y%whereYisasquarematrixwiththesamedimensionasJ.%Correspondingm-file:%functionf=lorenz_ext(t,X)%SIGMA=10;R=28;BETA=8/3;%x=X(1);y=X(2);z=X(3);%%Y=[X(4),X(7),X(10);%X(5),X(8),X(11);%X(6),X(9),X(12)];%f=zeros(9,1);%f(1)=SIGMA*(y-x);f(2)=
