Equivariant Hopf Bifurcation in a Ring of Identical Cells with Delay. (29th July 2009)

• Record Type: Journal Article
• Authors: Fan, Dejun; Wei, Junjie
• Other Names: He Ji Huan Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2009(2009)
• Publication Date: 2009-07-29
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2009/950251
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.