Heteroclinic cycles and wreath product symmetries

• Type: Article in International Scientific Journal
• Date: 2000

Authors

dias, aps (Author) FCUP; dionne, b (Author) Other; stewart, i (Author) Other

Journal

Title: Dynamics and Stability of Systems

Vol. 15

Pages: 353-385

ISSN: 0268-1110

Publisher: Oxford University Press

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 6 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-Y8M

DOI: 10.1080/713603760

Abstract (EN): We consider the existence and stability of heteroclinic cycles arising by local bifurcation in dynamical systems with wreath product symmetry Gamma = Z(2) integral G, where Z(2) acts by +/-1 on R and G is a transitive subgroup of the permutation group S-N (thus G has degree N). The group Gamma acts absolutely irreducibly on R-N. We consider primary (codimension one) bifurcations from an equilibrium to heteroclinic cycles as real eigenvalues pass through zero. We relate the possibility of such cycles to the existence of non-gradient equivariant vector fields of cubic order. Using Hilbert series and the software package MAGMA we show that apart from the cyclic groups G (previously studied by other authors) only five groups G of degree greater than or equal to7 are candidates for the existence of heteroclinic cycles. We establish the existence of certain types of heteroclinic cycle in these cases by making use of the concept of a subcycle. We also discusss edge cycles, and a generalization of heteroclinic cycles which we call a heteroclinic web. We apply our method to three examples.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 33