How to plot 2d and 3D phase portrait as in the image attachment for chaotic visualization? Also see my code.

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Farooq Aamir
Farooq Aamir 2024-3-5
编辑： Farooq Aamir 2024-3-6
function chaotic
% Define the parameters
k = 1;
lambda_1 = 1;
k_1 = 1;
k_2 = 2;
k_3 = 1;
v_1 = 0.4;
rho = 2;
omega = 1;
mu = 1;
% Calculate W_1 and W_2 based on the given parameters
W_1 = 6 * (k * lambda_1 + rho) / (3 * k * k_3 + 3 * k_2);
W_2 = (k^3 * k_3 + 3*k^2*k_2 + 6*(k*k_1 - v_1)) / (3 * k * k_3 + 3 * k_2);
% Define the time span
tspan = [0 100];
% Generate a grid of initial conditions
[G0, P0] = meshgrid(linspace(0, 0.2, 10), linspace(0, 0.2, 10));
initial_conditions = [G0(:), P0(:)];
% Prepare figures
figure('Name', '2D Phase Portrait');
figure('Name', '3D Phase Portrait');
% Loop over the initial conditions
for i = 1:size(initial_conditions, 1)
% Solve the ODE
[T, Y] = ode45(@(t, y) odesys(t, y, W_1, W_2, omega, mu), tspan, initial_conditions(i, :));
% Plot the 2D phase portrait
figure(findobj('Name', '2D Phase Portrait'));
plot(Y(:, 1), Y(:, 2));
hold on;
% Plot the 3D phase portrait
figure(findobj('Name', '3D Phase Portrait'));
plot3(T, Y(:, 1), Y(:, 2));
hold on;
end
% Finalize the 2D figure
figure(findobj('Name', '2D Phase Portrait'));
xlabel('G');
ylabel('P');
title('2D Phase Portrait');
grid on;
hold off;
% Finalize the 3D figure
figure(findobj('Name', '3D Phase Portrait'));
xlabel('Time');
ylabel('G');
zlabel('P');
title('3D Phase Portrait');
grid on;
hold off;
end
% Nested function for the system of ODEs
function dydt = odesys(t, y, W_1, W_2, omega, mu)
G = y(1);
P = y(2);
dGdt = P;
dPdt = W_1 * G^3 + W_2 * G + omega * cos(mu * t)^2;
dydt = [dGdt; dPdt];
end

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