Bifurcation of 3D system

39 次查看（过去 30 天）
Sarowar Hossain
Sarowar Hossain 2024-2-12
编辑： Anshuman 2024-9-9
I am working with a system of differential equations with three variable.Now, I need to check bifurcation of the system. I need a sample code for bifurcation of 3D system.

请先登录，再回答此问题。

回答（1 个）

Anshuman
Anshuman 2024-9-9
编辑：Anshuman 2024-9-9
Hello,
Typically for bifurcation analysis, tools like MATCONT are used. Below is a sample MATLAB script for a simple 3D system. This example assumes you have a system of differential equations and you want to perform bifurcation analysis by varying a parameter r. Here I am taking Lorenz system for using as an example.
% Define the system of differential equations
function dxdt = mySystem(t, x, r)
% Example system: Lorenz system
sigma = 10;
beta = 8/3;
dxdt = zeros(3,1);
dxdt(1) = sigma * (x(2) - x(1));
dxdt(2) = r * x(1) - x(2) - x(1) * x(3);
dxdt(3) = x(1) * x(2) - beta * x(3);
end
% Initial conditions and parameter
x0 = [1; 1; 1]; % Initial conditions for x, y, z
r = 28; % Initial parameter value
% Time span for the simulation
tspan = [0 100];
% Solve the system using ODE45 or any suitable solver
[t, x] = ode45(@(t, x) mySystem(t, x, r), tspan, x0);
% Plot the results
figure;
plot3(x(:,1), x(:,2), x(:,3));
xlabel('x');
ylabel('y');
zlabel('z');
title('3D System Dynamics');
grid on;
% For bifurcation analysis, you would typically use a tool like MATCONT
% Here, a simple parameter sweep is done
r_values = linspace(0, 50, 100); % Range of r for bifurcation analysis
bifurcation_points = [];
for r = r_values
[t, x] = ode45(@(t, x) mySystem(t, x, r), tspan, x0);
% Analyze the steady-state behavior, fixed points, etc.
% Here, you could check for changes in stability or periodicity
end
Hope it helps!

类别

在 Help Center 和 File Exchange 中查找有关 Nonlinear Dynamics 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by