Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 950251, 34 pages
Research Article

Equivariant Hopf Bifurcation in a Ring of Identical Cells with Delay

Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong 264209, China

Received 21 January 2009; Revised 27 March 2009; Accepted 24 May 2009

Academic Editor: Ji Huan He

Copyright © 2009 Dejun Fan and Junjie Wei. 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.


A kind of delay neural network with n elements is considered. By analyzing the distribution of the eigenvalues, a bifurcation set is given in an appropriate parameter space. Then by using the theory of equivariant Hopf bifurcations of ordinary differential equations due to Golubitsky et al. (1988) and delay differential equations due to Wu (1998), and combining the normal form theory of functional differential equations due to Faria and Magalhaes (1995), the equivariant Hopf bifurcation is completely analyzed.