Dynamics of Coupled Cell Networks: Synchrony, Heteroclinic Cycles and Inflation

• Tipo: Artigo em Revista Científica Internacional
• Data: 2011

Autores

aguiar, m (Autor) FCUP; ashwin, p (Autor) Outra; dias, a (Autor) FCUP; field, m (Autor) Outra

Revista

Título: Journal of Nonlinear Science

Vol. 21 Nº 2

Páginas: 271-323

ISSN: 0938-8974

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 68 Citações

Scopus - 71 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-002-SR4

DOI: 10.1007/s00332-010-9083-9

Abstract (EN): We consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focussing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible "inflations" of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 53