Studying Complexity for a Modified Dissipative Hamiltonian System: From Lyapunov Stability at the Origin to a Limit Cycle and Chaos

Hamiltonian formalism is commonly adopted to model a wide range of physical systems. In this paper, a particular case of a simple dissipative Hamiltonian system with modified damping matrix is analysed in terms of stability properties. It is shown that, dependent from the selected system parameters, we can obtain a system response that varies from a stable equilibrium at the origin, to a stable limit cycle and finally to chaotic behaviour.