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Coupled cell networks: Hopf bifurcation and interior symmetry

Pages: 71 - 78, Issue Special, September 2011

 Abstract        Full Text (144.0K)              

Fernando Antoneli - Universidade Federal de São Paulo (UNIFESP), Escola Paulista de Medicina, Escola Paulista de Medicina, Brazil (email)
Ana Paula S. Dias - Centro de Matemática da Universidade do Porto (CMUP) and Dep. de Matemática Pur, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal (email)
Rui Paiva - Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Leiria, Centro de Matemática da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal (email)

Abstract: We consider interior symmetric coupled cell networks where a group of permutations of a subset of cells partially preserves the network structure. In this setup, the full analogue of the Equivariant Hopf Theorem for networks with symmetries was obtained by Antoneli, Dias and Paiva (Hopf bifurcation in coupled cell networks with interior symmetries, SIAM J. Appl. Dynam. Sys. 7 (2008) 220–248). In this work we present an alternative proof of this result using center manifold reduction.

Keywords:  Hopf bifurcation, center manifold reduction, coupled cell systems. CMUP is supported by FCT through the programmes POCTI and POSI, with Portuguese and European Community structural funds.
Mathematics Subject Classification:  Primary: 34C15, 34C25, 37G40

Received: July 2010;      Revised: August 2010;      Published: October 2011.