Synchronization and relaxation for a class of globally coupled Hamiltonian systems

A class of coupled Hamiltonian systems is examined in which identical nonlinear oscillators are coupled through a mean field. The system is shown to have a steady desynchronized solution which becomes linearly unstable as the coupling strength is increased. We observe, in the stable case that the order parameter of the system decays to zero. For a wide class of initial conditions, the decay is exponential on an intermediate time scale and then as t(-3/2), as t --> infinity. This system shares many similarities to the Vlasov-Poisson equation and as well as Kuramoto's model. (C) 1998 Elsevier Science B.V.