Stable multisite periodic orbits in networks of weakly coupled bistable oscillators

The existence of multisite stable periodic orbits in infinite networks of w eakly coupled bistable oscillators is proved through a continuation process from the uncoupled limit. Using a Lyapunov-Schmidt reduction, it is shown that the stability of periodic orbits is determined by a finite-dimensional eigenvalue problem. As an application, the existence of N-site stable peri odic orbits in an infinite chain of coupled bistable oscillators is proved for any finite N. Moreover, the stability of spatially disordered periodic orbits is proved in infinite networks of coupled bistable oscillators with exponentially decaying couplings.