Hopf bifurcation in coupled cell networks with interior symmetries

• Type: Article in International Scientific Journal
• Date: 2008

Authors

antoneli, f (Author) Other; dias, aps (Author) FCUP; paiva, rc (Author) Other

Journal

Title: SIAM Journal on Applied Dynamical Systems

Vol. 7 No. 1

Pages: 220-248

ISSN: 1536-0040

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 23 Citations

Scopus - 25 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-004-4TK

DOI: 10.1137/070684604

Abstract (EN): We consider an important class of nonsymmetric networks that lies between the class of general networks and the class of symmetric networks, where group theoretic methods still apply-namely, networks admitting "interior symmetries." The main result of this paper is the full analogue of the equivariant Hopf theorem for networks with symmetries. We extend the result of Golubitsky, Pivato, and Stewart [Dyn. Syst., 19 (2004), pp. 389-407] to obtain states whose linearizations on certain subsets of cells, near bifurcation, are superpositions of synchronous states with states having spatio-temporal symmetries.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 29