Hopf Bifurcation diagram for 3D system
Hello I want to plot the Hopf bifurcation diagram, I have this code but I’m getting nothing other than straight lines.
% Parameters
r=3;
a=0.2;
b=2;
gamma=0.3;
m=0.92;
c=2.5;
alpha=10;
p=100.001;
q=0.01;
% Define the range of parameter values for bifurcation diagram
eta_values = linspace(0, 3, 1000); % Range of ‘eta’ values
% Arrays to store results
x_result = zeros(size(eta_values));
y_result = zeros(size(eta_values));
z_result = zeros(size(eta_values));
% Initial conditions (for detecting the Hopf bifurcation)
x0 = 1000;
y0 = 200;
z0 = 600;
% Iterate over each ‘eta’ value
for i = 1:length(eta_values)
eta = eta_values(i);
% Solve the system using ODE45
tspan = [0 1000]; % Time span for integration
odefun = @(t, Y) [r*Y(1)*(1-Y(1)/Y(3))-a*(1-m)*Y(1)*Y(2)/(1+gamma*(1-m)*Y(1));
b*(1-m)*Y(1)*Y(2)/(1+gamma*(1-m)*Y(1))-c*Y(2);
(Y(3)-alpha)*(p-Y(3))/(q+Y(3));];
[~, Y] = ode45(odefun, tspan, [x0; y0; z0]);
% Check for Hopf bifurcation (change in stability)
% Look for oscillatory behavior in the solution
if i > 1
if abs(Y(end, 1) – x_result(i-1)) > 0.01
fprintf(‘Hopf bifurcation detected at eta = %fn’, eta);
end
end
% Record the final values (or a characteristic of the solution)
x_result(i) = Y(end, 1);
y_result(i) = Y(end, 2);
z_result(i) = Y(end, 3);
end
% Plot the bifurcation diagram
figure;
plot(eta_values, x_result, ‘.k’, ‘MarkerSize’, 1);
hold on;
plot(eta_values, y_result, ‘.b’, ‘MarkerSize’, 1);
plot(eta_values, z_result, ‘.r’, ‘MarkerSize’, 1);
xlabel(‘eta’);
ylabel(‘Steady State Values’);
legend(‘x’, ‘y’, ‘z’);
title(‘Hopf Bifurcation Diagram’);
grid on;Hello I want to plot the Hopf bifurcation diagram, I have this code but I’m getting nothing other than straight lines.
% Parameters
r=3;
a=0.2;
b=2;
gamma=0.3;
m=0.92;
c=2.5;
alpha=10;
p=100.001;
q=0.01;
% Define the range of parameter values for bifurcation diagram
eta_values = linspace(0, 3, 1000); % Range of ‘eta’ values
% Arrays to store results
x_result = zeros(size(eta_values));
y_result = zeros(size(eta_values));
z_result = zeros(size(eta_values));
% Initial conditions (for detecting the Hopf bifurcation)
x0 = 1000;
y0 = 200;
z0 = 600;
% Iterate over each ‘eta’ value
for i = 1:length(eta_values)
eta = eta_values(i);
% Solve the system using ODE45
tspan = [0 1000]; % Time span for integration
odefun = @(t, Y) [r*Y(1)*(1-Y(1)/Y(3))-a*(1-m)*Y(1)*Y(2)/(1+gamma*(1-m)*Y(1));
b*(1-m)*Y(1)*Y(2)/(1+gamma*(1-m)*Y(1))-c*Y(2);
(Y(3)-alpha)*(p-Y(3))/(q+Y(3));];
[~, Y] = ode45(odefun, tspan, [x0; y0; z0]);
% Check for Hopf bifurcation (change in stability)
% Look for oscillatory behavior in the solution
if i > 1
if abs(Y(end, 1) – x_result(i-1)) > 0.01
fprintf(‘Hopf bifurcation detected at eta = %fn’, eta);
end
end
% Record the final values (or a characteristic of the solution)
x_result(i) = Y(end, 1);
y_result(i) = Y(end, 2);
z_result(i) = Y(end, 3);
end
% Plot the bifurcation diagram
figure;
plot(eta_values, x_result, ‘.k’, ‘MarkerSize’, 1);
hold on;
plot(eta_values, y_result, ‘.b’, ‘MarkerSize’, 1);
plot(eta_values, z_result, ‘.r’, ‘MarkerSize’, 1);
xlabel(‘eta’);
ylabel(‘Steady State Values’);
legend(‘x’, ‘y’, ‘z’);
title(‘Hopf Bifurcation Diagram’);
grid on; Hello I want to plot the Hopf bifurcation diagram, I have this code but I’m getting nothing other than straight lines.
% Parameters
r=3;
a=0.2;
b=2;
gamma=0.3;
m=0.92;
c=2.5;
alpha=10;
p=100.001;
q=0.01;
% Define the range of parameter values for bifurcation diagram
eta_values = linspace(0, 3, 1000); % Range of ‘eta’ values
% Arrays to store results
x_result = zeros(size(eta_values));
y_result = zeros(size(eta_values));
z_result = zeros(size(eta_values));
% Initial conditions (for detecting the Hopf bifurcation)
x0 = 1000;
y0 = 200;
z0 = 600;
% Iterate over each ‘eta’ value
for i = 1:length(eta_values)
eta = eta_values(i);
% Solve the system using ODE45
tspan = [0 1000]; % Time span for integration
odefun = @(t, Y) [r*Y(1)*(1-Y(1)/Y(3))-a*(1-m)*Y(1)*Y(2)/(1+gamma*(1-m)*Y(1));
b*(1-m)*Y(1)*Y(2)/(1+gamma*(1-m)*Y(1))-c*Y(2);
(Y(3)-alpha)*(p-Y(3))/(q+Y(3));];
[~, Y] = ode45(odefun, tspan, [x0; y0; z0]);
% Check for Hopf bifurcation (change in stability)
% Look for oscillatory behavior in the solution
if i > 1
if abs(Y(end, 1) – x_result(i-1)) > 0.01
fprintf(‘Hopf bifurcation detected at eta = %fn’, eta);
end
end
% Record the final values (or a characteristic of the solution)
x_result(i) = Y(end, 1);
y_result(i) = Y(end, 2);
z_result(i) = Y(end, 3);
end
% Plot the bifurcation diagram
figure;
plot(eta_values, x_result, ‘.k’, ‘MarkerSize’, 1);
hold on;
plot(eta_values, y_result, ‘.b’, ‘MarkerSize’, 1);
plot(eta_values, z_result, ‘.r’, ‘MarkerSize’, 1);
xlabel(‘eta’);
ylabel(‘Steady State Values’);
legend(‘x’, ‘y’, ‘z’);
title(‘Hopf Bifurcation Diagram’);
grid on; hopf, bifurcation MATLAB Answers — New Questions
