Collective dynamics in multi-population Hamiltonian systems

In this paper, we investigate measure synchronization (MS) in a two-population network of coupled metronomes system. The system consists of N identical metronomes placed on two swing boards, and the two swings are connected by spring of stiffness k. Metronomes on each swing represents a single population. We mainly study the collective dynamics of multi-population Hamiltonian induced by increased couplings, including inter-population and intra-population couplings. It is found that by tuning K for the inter-population coupling intensity and R for the intra-population coupling intensity, the system reaches various MS states at certain critical coupling intensities, including partial MS and complete MS. The occurrence of partial and complete MS are discussed particularly by analyzing the Poincare sections of the Hamiltonian system. In addition, we find correspondence in between the phase-locking dynamics and various MS transitions.