Hi Massimiliano,
I understand you want to calculate eigen values and eigen vectors for the given set of equations. I have created a sample code to solve the equations you provided, you can adjust the values of C1 and C2 before calculating the initial conditions using the eigen vectors.
% Define the system matrix A
A = [-0.4, 0;
0.4, -0.5];
% Calculate eigenvalues and eigenvectors
[eigenvectors, eigenvalues] = eig(A);
% Set the number of iterations (time steps)
num_iterations = 50;
% Initialize arrays to store the solutions
x_vals = zeros(1, num_iterations);
y_vals = zeros(1, num_iterations);
% Adjust C1 C2 and initial conditions using eigenvectors
C1 = 1;
C2 = 1;
initial_conditions = C1 * eigenvectors(:,1) + C2 * eigenvectors(:,2);
% Set initial values
x_vals(1) = initial_conditions(1);
y_vals(1) = initial_conditions(2);
% Iterate and compute the solution
for t = 2:num_iterations
Z = A * [x_vals(t-1); y_vals(t-1)];
x_vals(t) = Z(1);
y_vals(t) = Z(2);
end
% Plot the solutions
figure;
plot(0:num_iterations-1, x_vals);
figure;
plot(0:num_iterations-1, y_vals);
% Check if the system is in equilibrium
if all(abs(diag(eigenvalues)) < 1)
disp('The system is stable and the equilibrium X(T) = 0 is reached.');
else
disp('The system is unstable and the equilibrium X(T) = 0 is not reached.');
end
You may refer to the following documentation link for more information about “eig” function:
I hope this helps!
