Bifurcation of periodic solutions from a ring configuration ofdiscrete nonlinear oscillators

Carlos Garca-Azpeitia; Jorge Ize

doi:10.3934/dcdss.2013.6.975

Article Contents

2013, Volume 6, Issue 4: 975-983. Doi: 10.3934/dcdss.2013.6.975

This issue Previous Article Dynamics of the the dihedral four-body problem Next Article Equivariant Conley index versus degree for equivariant gradient maps

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

Carlos Garca-Azpeitia^1,2,3, and
Jorge Ize^1,2,3

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: August 2013

Abstract Related Papers Cited by

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 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.

Keywords:

Mathematics Subject Classification: 34C25, 37G40, 47H11, 54F45.

Citation:

Related Papers

Cited by

References

[1]	AIMS Series on Differential Equations & Dynamical Systems, 1. American Institute of Mathematical Sciences (AIMS), 2006.
[2]	in "Proceedings of the 3rd Conference on Localization and Energy Transfer in Nonlinear Systems" (editor, Luis Vázquez), 44-67. NJ: World Scientific, Singapore, (2003).
[3]	UNAM. PhD thesis, 2010.
[4]	Journal of Differential Equations, 251 (2011), 3202-3227.doi: 10.1016/j.jde.2011.06.021.
[5]	Preprint, 2012.
[6]	Journal of Differential Equations, 252 (2012), 5662-5678.doi: 10.1016/j.jde.2012.01.044.
[7]	in "Topological Nonlinear Analysis" Progr. Nonlinear Differential Equations Appl., 15, 341-463. Birkhäuser Boston, (1995).
[8]	De Gruyter Series in Nonlinear Analysis and Applications, 8. Walter de Gruyter, Berlin, 2003.doi: 10.1515/9783110200027.
[9]	J. Phys. A: Math. Gen., 37 (2004), 2201-2222.doi: 10.1088/0305-4470/37/6/017.
[10]	Nonlinearity, 7 (1994), 1623-1643.
[11]	Phys. Lett. A, 374 (2010), 3912-1919.doi: 10.1016/j.physleta.2010.07.022.
[12]	Physica D., 238 (2009), 687-698.doi: 10.1016/j.physd.2009.01.001.
[13]	Milan J. Math., 73 (2005), 103-144.doi: 10.1007/s00032-005-0040-2.