耦合振荡器系统的最大李雅普诺夫指数 (LLE) 谱matlab代码.rar

%{ calculation of the largest lyapunov exponent (lle) by the method suggested by J.C.Sprott, Department of Physics, University of Wisconsin, Madison, WI 53706, USA %} % http://sprott.physics.wisc.edu/chaos/lyapexp.htm %{ used to find the lyapunov exponent spectrum of a system of nonlinearly coupled oscillators as the coupling parameter is varied %} global be; global gm; %'gm' and 'be' are the parameters of the system be=1; c1=1; lya3=zeros(101,2); %stores the lle and the corresponding value of gm for gm=10:0.05:40 %any range may be chosen by the user c=1; t0=0; tf=8; N=80; E=0.2; px=0.2; x1=0; x2=px; x3=0; x4=sqrt(2*E-(px^2)); %(x1,x2,x3,x4) and (x11,x22,x33,x44) are arbitrarily close initial conditions x11=10^-8; x22=px+10^-8; x33=10^-8; x44=x4+10^-8; d0=sqrt((x11-x1)^2+(x22-x2)^2+(x33-x3)^2+(x44-x4)^2); % initial separation between the trajectories lam=zeros(401,1); % stores the exponent calculated at each iteration for i=1:400 %solving the equations of the system of interest for each of the trajectories [t,x] = ode_RK4_Yang([t0 tf],[x1 x2 x3 x4],N); [tt,xx] = ode_RK4_Yang([t0 tf],[x11 x22 x33 x44],N); d1=sqrt((xx(81,1)-x(81,1))^2+(xx(81,2)-x(81,2))^2+(xx(81,3)-x(81,3))^2+(xx(81,4)-x(81,4))^2); %separation at the end of each iteration lam(c,1)=log(d1/d0); %reinitialization of the trajectories after each iteration x11=x(81,1)+(xx(81,1)-x(81,1))*(d0/d1); x22=x(81,2)+(xx(81,2)-x(81,2))*(d0/d1); x33=x(81,3)+(xx(81,3)-x(81,3))*(d0/d1); x44=x(81,4)+(xx(81,4)-x(81,4))*(d0/d1); x1=x(81,1); x2=x(81,2); x3=x(81,3); x4=x(81,4); t0=tf; tf=tf+8; c=c+1; end lya3(c1,1)=mean(lam(100:400)); % finally lle is the mean of all the calculated exponents lya3(c1,2)=gm; c1=c1+1; end