Bifurcation of periodic solutions from a ring configuration of discrete nonlinear oscillators

Abstract: This paper gives an analysis of the periodic solutions of a ring of $n$ oscillators coupled to their neighbors. We prove the bifurcation of branches of such solutions from a relative equilibrium, and we study their symmetries. We give complete results for a cubic Schr\"odinger potential and for a saturable potential and for intervals of the amplitude of the equilibrium. The tools for the analysis are the orthogonal degree and representation of groups. The bifurcation of relative equilibria was given in a previous paper.