Dynamics of coupled oscillators with convex interaction potential

In this paper we study via the monotonicity approach the dynamical behavior of a class of coupled oscillators with periodic on-site potential and convex interaction potential. It is shown that under periodic or Neumann boundary conditions the Poincare map admits an invariant curve, on which the Poincare map is actually an orientation preserving circle homeomorphism. Some consequences are then obtained, including a Massera type theorem and the existence of running periodic solutions. For the Dirichlet boundary conditions, each solution is asymptotic to a periodic solution if it is not periodic. (C) 2010 American Institute of Physics. [doi:10.1063/1.3489424]