Linear Expansions of Dynamical Systems With Degenerate Matrix on a Torus

Key Points

• The linear expansions reveal important behaviors of dynamical systems under a degenerate matrix, impacting stability.
• Key findings indicate that the eigenvalues associated with the degenerate matrix significantly affect stability outcomes.
• Analysis of parameter space was conducted on a torus, providing insights into how these systems behave globally.
• The results highlight the importance of understanding matrix degeneracy in addressing stability in dynamical systems.