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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 417678, 10 pages
http://dx.doi.org/10.1155/2013/417678
Research Article

Multiple Nonlinear Oscillations in a -Symmetrical Coupled System of Identical Cells with Delays

College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, China

Received 31 January 2013; Accepted 8 May 2013

Academic Editor: Zhiming Guo

Copyright © 2013 Haijun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A coupled system of nine identical cells with delays and -symmetry is considered. The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. By analyzing the corresponding characteristic equations, the linear stability of the equilibrium is given. We also investigate the simultaneous occurrence of multiple periodic solutions and spatiotemporal patterns of the bifurcating periodic oscillations by using the equivariant bifurcation theory of delay differential equations combined with representation theory of Lie groups. Numerical simulations are carried out to illustrate our theoretical results.