December  2006, 16(4): 923-960. doi: 10.3934/dcds.2006.16.923

Applied equivariant degree. part II: Symmetric Hopf bifurcations of functional differential equations

1. 

Department of Mathematics and Computer Sciences, Netanya Academic College, Netanya 42365

2. 

Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

Received  June 2005 Revised  August 2006 Published  September 2006

In this paper we apply the equivariant degree method to the Hopf bifurcation problem for a system of symmetric functional differential equations. Local Hopf bifurcation is classified by means of an equivariant topological invariant based on the symmetric properties of the characteristic operator. As examples, symmetric configurations of identical oscillators, with dihedral, tetrahedral, octahedral, and icosahedral symmetries, are analyzed.
Citation: Zalman Balanov, Meymanat Farzamirad, Wieslaw Krawcewicz, Haibo Ruan. Applied equivariant degree. part II: Symmetric Hopf bifurcations of functional differential equations. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 923-960. doi: 10.3934/dcds.2006.16.923
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