% Define the differential equation

function dxdt = myODE(t, x, a)

% Define the parameters

alpha = a(1);

beta = a(2);

% Define the dynamical system

dxdt = [alpha * x(1) - beta * x(1)^3];

end

% Define parameter range and initial condition

alpha_values = linspace(-2, 2, 100); % Range of alpha values

beta = 1; % Fixed beta value

x0 = 0.1; % Initial condition

% Iterate over parameter values and solve ODEs

for i = 1:length(alpha_values)

% Define current parameter set

a = [alpha_values(i), beta];

% Solve ODE

[t, x] = ode45(@(t,x) myODE(t,x,a), [0, 20], x0);

% Plot phase portrait

plot(x(:,1), x(:,2));

hold on;

end

% Labeling and formatting

xlabel('x');

ylabel('dx/dt');

title('Phase Portrait');

grid on;

hold off;

##In this code:

• myODE is a function that defines your ordinary differential equation system. In this example, it's a simple one-dimensional dynamical system.
• alpha_values defines a range of parameter values over which you want to perform the bifurcation analysis.
• ode45 is used to solve the ODE system numerically for each parameter value.
• The resulting phase portrait is plotted.