BIFURCATIONS IN RING ARRAYS OF PHASE-BISTABLE SYSTEMS

Abstract

This paper considers a system of identical parametric oscillators linearly coupled together in a ring geometry. The phase of the coupling is chosen so that the system takes on steady, rather than oscillatory, states, and this work focuses on the sequence of bifurcations from the zero steady state. Center manifold expressions are given for the forms of the solutions that emerge from these bifurcations, and full expressions are given for special cases. Secondary bifurcations are also briefly discussed.