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分数阶混沌系统李雅普指数和分岔图

山竹山竹px 2022-08-09 阅读 73

1、内容简介


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2、内容说明


%1. Chen's system:

[t, y]=FOChen([35 3 28 -7], [0.9 0.9 0.9], 100, [-9 -5 14]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%2. CNN - 3 cells net:

[t, y]=FO3CNN([1.24 1.1 1.0 4.4 3.21], [0.99 0.99 0.99], 100, [0.1 0.1 0.1]);

figure

plot3(y(:,1), y(:,2), y(:,3), 'k');

xlabel('x_1(t)'); ylabel('x_2(t)'); zlabel('x_3(t)'); grid;


%3. Arneodo's system:

[t,y]=FOArneodo([-5.5 3.5 0.8 -1.0], [0.97 0.97 0.96], 200, [-0.2 0.5 0.2]);

figure

plot3(y(:,1), y(:,2), y(:,3), 'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%4. Genesio-Tesi's system:

[t, y]=FOGenTesi([1.1 1.1 0.45 1.0], [1 1 0.95], 200, [-0.1 0.5 0.2]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%5. Lorenz's system:

[t, y]=FOLorenz([10 28 8/3],[0.993 0.993 0.993],100,[0.1 0.1 0.1]);

figure

plot3(y(:,1), y(:,2), y(:,3), 'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%6. Newton-Leipnik's system:

[t, y]=FONewLeipnik([0.4 0.175], [0.95 0.95 0.95], 200, [0.19 0 -0.18]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%7. Rossler's system:

[t, y]=FORossler([0.5 0.2 10], [0.9 0.85 0.95], 120, [0.5 1.5 0.1]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%8. Lotka-Volterra system:

[t, y]=FOLotkaVolterra([1 1 1 1 2 3 2.7], [0.95 0.95 0.95], 200, [1 1.4 1]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%9. Duffing's system:

[t, y]=FODuffing([0.15 0.3 1], [0.9 1], 200, [0.21 0.31]);

figure

plot(y(:,1), y(:,2), 'k');

xlabel('x(t)'); ylabel('y(t)'); grid;


%10. Van der Pol's oscillator:

[t, y]=FOvanDerPol(1, [1.2 0.8], 60, [0.2 -0.2]);

figure

plot(y(:,1), y(:,2), 'k');

xlabel('y_1(t)'); ylabel('y_2(t)'); grid;


%11. Volta's system:

[t, y]=FOVolta([19 11 0.73],[0.99 0.99 0.99], 20, [8 2 1]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%12. Lu's system:

[t, y]=FOLu([36 3 20], [0.985 0.99 0.98], 60, [0.2 0.5 0.3]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%13. Liu's system:

[t, y]=FOLiu([1 2.5 5 1 4 4], [0.95 0.95 0.95], 100, [0.2 0 0.5]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;


%14. Chua's systems:

[t, y]=FOChuaNR([10.725 10.593 0.268 -0.7872 -1.1726], [0.93 0.99 0.92], 60, [0.6 0.1 -0.6]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;

[t, y]=FOChuaM([10 13 0.1 1.5 0.3 0.8], [0.97 0.97 0.97 0.97], 200, [0.8 0.05 0.007 0.6]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;

figure

plot3(y(:,4), y(:,1), y(:,2),'k');

xlabel('w(t)'); ylabel('x(t)'); zlabel('y(t)'); grid;


%15. Financial system:

[t, y]=FOFinanc([1 0.1 1],[1 0.95 0.99],200, [2 -1 1]);

figure

plot3(y(:,1), y(:,2), y(:,3),'k');

xlabel('x(t)'); ylabel('y(t)'); zlabel('z(t)'); grid;

3、仿真分析

分数阶混沌系统李雅普指数和分岔图_3c

 

分数阶混沌系统李雅普指数和分岔图_3c_02

 

分数阶混沌系统李雅普指数和分岔图_3c_03

 

分数阶混沌系统李雅普指数和分岔图_3c_04

 

4、参考论文


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