duffing_bifurcation.m

duffing混沌振子的实现代码

% Author: Thomas Lee

% E-mail: [e-mail] % Corresponding: School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China 

 

 
% 
% function dx=duffing(t,X)
% 
% global F wd;
% 
% %r=0.168;
% r=0.5;
% 
% x=X(1);
% 
% y=X(2);
% 
% psi=X(3);
% 
% dx=zeros(3,1);
% 
% dx(1)=y;
% 
% %dx(2)=-r*y+1/2*x*(1-x^2)+F*sin(psi);
% dx(2)=-r*y+x*(1-x^2)+F*sin(psi);
% 
% dx(3)=wd;

 

 

function duffing_bifurcation() 

clear;

global F wd;

wd=1.0;

range=[0.10:0.01:1.0];

period=2*pi/wd; % 

k=0;

YY2=[];

step=2*pi/100;  %步长。

for F=range

    y0=[0 0 0];

   F

    k=k+1;

    % discard the first 60 periodic data;

    %除去前面60个周期的数据，并将最后的结果作为下一次积分的初值

    tspan=[0:step:60*period];

    [t,Y]=ode45(@duffing,tspan,y0);

    y0=Y(end,:);

    j=1;

    for i=60:200

        tspan=[i*period:step:(i+1)*period];

        [t,Y]=ode45(@duffing,tspan,y0);

        YY1(k,j)=Y(end,1);   % get the omega data from every period end

        j=j+1;               %取出每一个周期内的第一个解的最后一个值。

        y0=Y(end,:);

    end

end

bifdata=YY1(:,end-51:end);

plot(range,bifdata,'b.','markersize',1);