# American Institute of Mathematical Sciences

August  2013, 6(4): 975-983. doi: 10.3934/dcdss.2013.6.975

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

 1 Depto. Matemticas y Mecnica 2 IIMAS-UNAM, FENOMEC 3 Apdo. Postal 20-726, 01000 Mxico D.F.

Received  October 2011 Revised  April 2012 Published  December 2012

This paper gives an analysis of the periodic solutions of a ring of $n$oscillators coupled to their neighbors. We prove the bifurcation of branchesof such solutions from a relative equilibrium, and we study theirsymmetries. We give complete results for a cubic Schr?dinger potential andfor a saturable potential and for intervals of the amplitude of theequilibrium. The tools for the analysis are the orthogonal degree andrepresentation of groups. The bifurcation of relative equilibria was givenin a previous paper.
Citation: Carlos Garca-Azpeitia, Jorge Ize. Bifurcation of periodic solutions from a ring configuration of discrete nonlinear oscillators. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 975-983. doi: 10.3934/dcdss.2013.6.975
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