jose_ly.m

基于Matlab对约瑟夫森结（Josephson Junction）RCSJ模型的交直流I-V特性及非线性混沌现象进行数值模拟。通过计算机数值模拟得到该模型的非线性微分方程数值解

%
function ly=jose_ly(b,k)
% the largest lyapunov exponent of josephson
% k 迭代步数，b 参数
% 方程如下:
%   θ''+G*θ'+sinθ=I+A*sin(ωt)+αsin(βωt)
% 变化：
%   dx=y
%   dy=-G*y-sin(x)+I+A*sin(w*t)+a*sin(b*w*t)
%
% Example:
%   ly=jose_ly(0,800)
%
% Author:LDYU
% Author's email: [e-mail]
%
global Bc ia w id; 
d0=1e-8;
ly=0;
lsum=0;
x=[0;2;b];
x1=[d0;2;b];
for t=1:k
   [T1,Y1]=ode45('Josephson_Junction',[t-1,t],x);
   [T2,Y2]=ode45('Josephson_Junction',[t-1,t],x1);
   x=Y1(end,:);
   x1=Y2(end,:);
   d1=norm(x-x1);
   x1=x+(d0/d1)*(x1-x);
   lsum=lsum+log(d1/d0);
end
ly=lsum/k;