UNSPECIFIED (2000) Heteroclinic cycles and wreath product symmetries. DYNAMICS AND STABILITY OF SYSTEMS, 15 (4). pp. 353-385. ISSN 0268-1110

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery
Journal or Publication Title:	DYNAMICS AND STABILITY OF SYSTEMS
Publisher:	TAYLOR & FRANCIS LTD
ISSN:	0268-1110
Date:	December 2000
Volume:	15
Number:	4
Number of Pages:	33
Page Range:	pp. 353-385
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/12512

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