Homogeneous coupled cell networks with S3-Symmetric quotient

• Tipo: Artigo em Revista Científica Internacional
• Data: 2007

Autores

aguiar, mad (Autor) FEP; dias, aps (Autor) FCUP; golubitsky, m (Autor) Outra; leite, mca (Autor) Outra

Revista

Título: Discrete and Continuous Dynamical Systems

Páginas: 1-9

ISSN: 1078-0947

Editora: American Institute of Mathematical Sciences

Indexação

ISI Web of Knowledge

Scopus - 8 Citações

Outras Informações

ID Authenticus: P-007-SJK

Abstract (EN): A coupled cell network represents dynamical systems (the coupled cell systems) that can be seen as a set of individual dynamical systems (the cells) with interactions between them. Every coupled cell system associated to a network, when restricted to a flow-invariant subspace defined by the equality of certain cell coordinates, corresponds to a coupled cell system associated to a smaller network, called quotient network. In this paper we consider homogeneous networks admitting a S3-symmetric quotient network. We assume that a codimension-one synchrony-breaking bifurcation from a synchronous equilibrium occurs for that quotient network. We aim to investigate, for different networks admitting that S3-symmetric quotient, if the degeneracy condition leading to that bifurcation gives rise to branches of steady-state solutions outside the flow-invariant subspace associated with the quotient network. We illustrate that the existence of new solutions can be justified directly or not by the symmetry of the original network. The bifurcation analysis of a six-cell asymmetric network suggests that the existence of new solutions outside the flow-invariant subspace associated with the quotient is 'forced' by the symmetry of a five-cell quotient network.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 9