@article {Dias:1 December 2000:0268-1110:353,
	author = "Dias A.P. S.",
	author = "Dionne B.",
	author = "Stewart I.",
	title = "Heteroclinic cycles and wreath product symmetries",
	journal = "Dynamics and Stability of Systems",
	volume = "15",
	year = "1 December 2000",
	abstract = "We consider the existence and stability of heteroclinic cycles arising by local bifurcation in dynamical systems with wreath product symmetry = Z<SUB>2</SUB> G, where Z<SUB>2</SUB> acts by &#177; 1 on R and G is a transitive subgroup of the permutation group S<SUB>N</SUB> (thus G has degree N). The group acts absolutely irreducibly on R<SUB>N</SUB>. 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 <IMG SRC="/iso-ents/isotech/le.gif" ALT="le">7 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.",
	pages = "353-385(33)",
	url = "http://www.ingentaconnect.com/content/tandf/cdssold/2000/00000015/00000004/art00003"
}