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

Pages: 923 - 960, Volume 16, Issue 4, December 2006

doi:10.3934/dcds.2006.16.923       Abstract        Full Text (370.8K)       Related Articles

Zalman Balanov - Department of Mathematics and Computer Sciences, Netanya Academic College, Netanya 42365, Israel (email)
Meymanat Farzamirad - Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada (email)
Wieslaw Krawcewicz - Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada (email)
Haibo Ruan - Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada (email)

Abstract: 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.

Keywords:  Equivariant degree, symmetric systems of FDEs, Hopf bifurcation with symmetries, basic maps, isotypical crossing numbers, configurations of identical oscillators, dihedral, tetrahedral, octahedral and icosahedral symmetries.
Mathematics Subject Classification:  Primary: 34C25; Secondary: 47J05.

Received: June 2005;      Revised: August 2006;      Published: September 2006.