# American Institute of Mathematical Sciences

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2011, 2011(Special): 71-78. doi: 10.3934/proc.2011.2011.71

## Coupled cell networks: Hopf bifurcation and interior symmetry

 1 Universidade Federal de São Paulo (UNIFESP), Escola Paulista de Medicina, Escola Paulista de Medicina, Brazil 2 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 3 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

Received  July 2010 Revised  August 2010 Published  October 2011

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.
Citation: Fernando Antoneli, Ana Paula S. Dias, Rui Paiva. Coupled cell networks: Hopf bifurcation and interior symmetry. Conference Publications, 2011, 2011 (Special) : 71-78. doi: 10.3934/proc.2011.2011.71
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