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找几个混沌时间序列，无意间发现的Matlab程序，适合初学者
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序列一：Chen 等式

效果图

Matlab代码

clc;
clear;

a=35;
b=3;
c=28;
x(1)=0;
y(1)=1.001;
z(1)=0;
h=0.0001;
for i=1:100000
    K1=a*(y(i)-x(i));
    L1=(c-a)*x(i)-x(i)*z(i)+c*y(i);
    M1=x(i)*y(i)-b*z(i);

    K2=a*((y(i)+h/2*L1)-(x(i)+h/2*K1));
    L2=(c-a)*(x(i)+h/2*K1)-(x(i)+h/2*K1)*(z(i)+h/2*M1)+c*(y(i)+h/2*L1);
    M2=(x(i)+h/2*K1)*(y(i)+h/2*L1)-b*(z(i)+h/2*M1);

    K3=a*((y(i)+h/2*L2)-(x(i)+h/2*K2));
    L3=(c-a)*(x(i)+h/2*K2)-(x(i)+h/2*K2)*(z(i)+h/2*M2)+c*(y(i)+h/2*L2);
    M3=(x(i)+h/2*K2)*(y(i)+h/2*L2)-b*(z(i)+h/2*M2);

    K4=a*((y(i)+h*L3)-(x(i)+h*K3));
    L4=(c-a)*(x(i)+h*K3)-(x(i)+h*K3)*(z(i)+h*M3)+c*(y(i)+h*L3);
    M4=(x(i)+h*K3)*(y(i)+h*L3)-b*(z(i)+h*M3);

    x(i+1)=x(i)+h/6*(K1+2*K2+2*K3+K4);
    y(i+1)=y(i)+h/6*(L1+2*L2+2*L3+L4);
    z(i+1)=z(i)+h/6*(M1+2*M2+2*M3+M4);
end
%for j=1:250000
%   x(j)=x(10000+j);
%   y(j)=y(10000+j);
%   z(j)=z(10000+j);
%end
figure(1);
plot3(x,y,z);
title('Chen等式的三维相空间吸引子');
xlabel('X(t)');
ylabel('Y(t)');
zlabel('Z(t)');
grid;
figure(2);
plot(x);
title('Chen等式的X相序列');
xlabel('t');
Ylabel('X(t)');
grid;
x2=x';

序列二：Logistic

效果图

Matlab代码

clc;
clear;

x=0.1;
u=2:0.001:4;
for i=1:2000
    x=u.*(x-x.^2);
  if i>=1900
    plot(u,x);
    title('Logistic Map');
    xlabel('a');
    ylabel('X(n)');
    hold on;
  end
end

序列三：Lorenz （洛伦兹）

效果图

Matlab代码

clc;
clear;

p=10;
r=28;
b=8/3;
x(1)=10;
y(1)=1;
z(1)=0;
h=0.01;
for i=1:1:10000
    K1=p*(y(i)-x(i));
    L1=r*x(i)-y(i)-x(i)*z(i);
    M1=-b*z(i)+x(i)*y(i);
    
    K2=p*((y(i)+h/2*L1)-(x(i)+h/2*K1));
    L2=r*(x(i)+h/2*K1)-(y(i)+h/2*L1)-(x(i)+h/2*K1)*(z(i)+h/2*M1);
    M2=-b*(z(i)+h/2*M1)+(x(i)+h/2*K1)*(y(i)+h/2*L1);
    
    K3=p*((y(i)+h/2*L2)-(x(i)+h/2*K1));
    L3=r*(x(i)+h/2*K1)-(y(i)+h/2*L2)-(x(i)+h/2*K1)*(z(i)+h/2*M2);
    M3=-b*(z(i)+h/2*M1)+(x(i)+h/2*K1)*(y(i)+h/2*L2);
    
    K4=p*((y(i)+h*L3)-(x(i)+h*K3));
    L4=r*(x(i)+h*K3)-(y(i)+h*L3)-(x(i)+h*K3)*(z(i)+h*M3);
    M4=-b*(z(i)+h*M3)+(x(i)+h*K3)*(y(i)+h*L3);
    
    x(i+1)=x(i)+h/6*(K1+2*K2+2*K3+K4);
    y(i+1)=y(i)+h/6*(L1+2*L2+2*L3+L4);
    z(i+1)=z(i)+h/6*(M1+2*M2+2*M3+M4);
end
figure(1);
plot3(x,y,z);
xlabel('x(t)'),ylabel('y(t)'),zlabel('z(t)');
title('Lorenz吸引子图');
figure(2);
plot(x);
xlabel('t'),ylabel('x(t)')
title('Lorenz X相时间序列');
figure(3)
plot(y);
xlabel('t'),ylabel('y(t)')
title('Lorenz Y相时间序列');
figure(4)
plot(x);
xlabel('t'),ylabel('z(t)')
title('Lorenz Z相时间序列');
N=length(x);
m=3;
tau=1;
P=N-(m-1)*tau;
for ii=1:m
   for jj=1:P
       data(jj,ii)=x(jj+(ii-1)*tau);
   end
end
y1=data(:,1);
y2=data(:,2);
y3=data(:,3);
figure(5);
plot3(y1,y2,y3);
legend('tau=10');
xlabel('x(t+tau)'),ylabel('x(t+tau)'),zlabel('x(t+2*tau)');
title('Lorenz X相三维重构吸引子图');

序列四：rossler

效果图

Matlab程序

clc;
clear;


a=0.2;
b=0.4;
c=5.7;		%改变C可以生成混沌序列
x(1)=1;
y(1)=0;
z(1)=0;
h=0.01;

for i=1:20000
    K1=-(y(i)+z(i));
    L1=x(i)+a*y(i);
    M1=b+x(i)*z(i)-c*z(i);

    K2=-((y(i)+h/2*L1)+(z(i)+h/2*M1));
    L2=(x(i)+h/2*K1)+a*(y(i)+h/2*L1);
    M2=b+(x(i)+h/2*K1)*(z(i)+h/2*M1)-c*(z(i)+h/2*M1);

    K3=-((y(i)+h/2*L2)+(z(i)+h/2*M2));
    L3=(x(i)+h/2*K2)+a*(y(i)+h/2*L2);
    M3=b+(x(i)+h/2*K2)*(z(i)+h/2*M2)-c*(z(i)+h/2*M2); 

    K4=-((y(i)+h*L3)+(z(i)+h*M3));
    L4=(x(i)+h*K3)+a*(y(i)+h*L3);
    M4=b+(x(i)+h*K3)*(z(i)+h*M3)-c*(z(i)+h*M3);  

    x(i+1)=x(i)+h/6*(K1+2*K2+2*K3+K4);
    y(i+1)=y(i)+h/6*(L1+2*L2+2*L3+L4);
    z(i+1)=z(i)+h/6*(M1+2*M2+2*M3+M4);
end
figure(1);
plot3(x,y,z);
title('Rossler等式的三维相空间吸引子');
xlabel('X(t)');
ylabel('Y(t)');
zlabel('Z(t)');
grid;
figure(2);
plot(x);
title('Rossler等式的X相序列');
xlabel('t');
Ylabel('X(t)');
grid;
x=x';
y=y';
z=z';