Local bifurcation in symmetric coupled cell networks: Linear theory

• Type: Article in International Scientific Journal
• Date: 2006

Authors

dias, aps (Author) FCUP; lamb, jsw (Author) Other

Journal

Title: Physica D: Nonlinear Phenomena

Vol. 223

Pages: 93-108

ISSN: 0167-2789

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 24 Citations

Scopus - 29 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-004-GEW

DOI: 10.1016/j.physd.2006.08.014

Abstract (EN): We consider a coupled cell network of differential equations with finite symmetry group Gamma, where Gamma permutes cells transitively. We show how the structure of the coupled cell network, represented by a directed graph whose vertices represent individual cells and edges represent couplings, can be taken into account in the bifurcation analysis of a fully symmetric steady-state solution. We focus on the analysis of the linearized vector field at a fully symmetric equilibrium and show that in the case of active cells, if Gamma is Abelian the network structure does not influence the types of codimension one local bifurcations. We also show that beyond this context, when Gamma is not Abelian, cells are passive, or when considering local bifurcations of higher codimensions, anomalies due to the network structure may arise.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16