% Bifurcation diagram for a 1D dynamical system

% Define the dynamical system

f = @(x, r) r * x - x^3; % Example: x' = r*x - x^3

% Set parameter range and values

r_values = linspace(-2, 2, 1000); % Parameter values

x_transient = 100; % Number of transient iterations

x_values = zeros(1, length(r_values));

% Perform numerical simulations for each parameter value

for i = 1:length(r_values)

r = r_values(i);

x = 0.1; % Initial condition

% Transient iterations

for j = 1:x_transient

x = f(x, r);

end

% Collect data for bifurcation diagram

x_values(i) = x;

end

% Plot the bifurcation diagram

figure;

plot(r_values, x_values, '.', 'MarkerSize', 1);

xlabel('Parameter (r)');

ylabel('Steady-State Value (x)');

title('Bifurcation Diagram');

grid on;

credit : openai

See here for discrete time systems, there is a code in the description https://www.youtube.com/watch?v=JgLyk304MYk

Lazaros Moysis thank you for your response and needful behaviour.