pyoculus.solvers.manifold.eig

pyoculus.solvers.manifold.eig(jacobian)

Compute stable and unstable eigenvalues/eigenvectors of a fixed point.

This function calculates the eigenvalues and eigenvectors of a given Jacobian matrix and separates them into stable and unstable components based on their magnitudes.

Parameters:

jacobian (np.ndarray) – A 2x2 Jacobian matrix at the fixed point.

Returns:

lambda_s (float): The stable eigenvalue (\(\vert\lambda\vert < 1\)) vector_s (np.ndarray): The corresponding stable eigenvector lambda_u (float): The unstable eigenvalue (\(\vert\lambda\vert > 1\)) vector_u (np.ndarray): The corresponding unstable eigenvector

Return type:

tuple

Examples

>>> J = np.array([[1.5, 0.5], [0.5, 2.0]])
>>> lambda_s, v_s, lambda_u, v_u = eig(J)