{The analysis of solitonic, supernonlinear, periodic,
quasiperiodic, bifurcation and chaotic patterns of perturbed
Gerdjikov–Ivanov model with full nonlinearity} this is the name of paper where the dynamical model is define in eq 34
% 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.
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