matlab混沌仿真

Question

matlab混沌仿真
参数变化时的分岔图和李普亚诺夫指数谱图

当固定参数b=3，参数a在0到2区间变化时，x和y随参数a变化时的分岔图和李普亚诺夫指数谱图
当固定参数a=1，参数b在0到4区间变化时，x和y随参数b 变化时的分岔图和李普亚诺夫指数谱图
能用matlab仿真出来吗

Answer 1

该回答引用ChatGPT GPT-4

运行结果

代码

clear;
clc;

% Parameters
a_min = 0;
a_max = 2;
b_fixed = 3;
num_a_values = 1000;
num_iterations = 1000;
num_transients = 100;

% Initialize arrays
a_values = linspace(a_min, a_max, num_a_values);
x_values = zeros(num_a_values, num_iterations);
y_values = zeros(num_a_values, num_iterations);

% Bifurcation diagram for fixed b
for i = 1:num_a_values
    a = a_values(i);
    b = b_fixed;
    x = rand; % Random initial condition
    y = rand;

    % Remove transient iterations
    for t = 1:num_transients
        [x, y] = chaotic_system(a, b, x, y);
    end

    % Record iterations
    for t = 1:num_iterations
        [x, y] = chaotic_system(a, b, x, y);
        x_values(i, t) = x;
        y_values(i, t) = y;
    end
end

figure(1);
plot(a_values, x_values, '.');
title('Bifurcation Diagram for x (Fixed b)');
xlabel('a');
ylabel('x');

figure(2);
plot(a_values, y_values, '.');
title('Bifurcation Diagram for y (Fixed b)');
xlabel('a');
ylabel('y');

% 要计算李普诺夫指数，您可以使用现有的函数，如 "nolds" 库。首先，安装 "nolds" 库：
% https://www.mathworks.com/matlabcentral/fileexchange/70178-nolds

% 下面是计算李普诺夫指数谱图的示例代码：
% 注意，这需要安装 "nolds" 库。

% lyap_x = zeros(num_a_values, 1);
% lyap_y = zeros(num_a_values, 1);

% for i = 1:num_a_values
%     lyap_x(i) = nolds('lyap_r', x_values(i, :));
%    

function [x_next, y_next] = chaotic_system(a, b, x, y)
    x_next = a * (sin(pi * y) + b) * x * (1 - x);
    y_next = a * (sin(pi * x + 1) + b) * y * (1 - y);
end