Measure synchronization in coupled Duffing Hamiltonian systems

We examine the collective behaviour of coupled Duffing Hamiltonian systems (HS) and show the existence of measure synchronization (MS) in the quasi-periodic (QP) and -chaotic states. We show that the dynamics of coupled Duffing Hamiltonians exhibit a transition to coherent invariant measure, their orbits sharing the same phase space as the coupling strength is increased. Transitions from QP measure desynchronous to QP MS state and QP measure desynchronous to chaotic measure synchronous (CMS) state were both identified. Moreover, a transition from partial measure synchronization state to complete CMS state was found for three coupled subsystems.