Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria
University of Exeter
International Journal of Bifurcation and Chaos
World Scientific Publishing Company
Robust attracting heteroclinic cycles have been found in many models of dynamics with symmetries. In all previous examples, robust heteroclinic cycles appear between a number of symmetry broken equilibria. In this paper we examine the first example where there are robust attracting heteroclinic cycles that include the origin, ie a point with maximal symmetry. The example we study is for vector fields on R3 with (Z2)3 symmetry. We list all possible generic (codimension one) local and global bifurcations by which this cycle can appear as an attractor; these include a resonance bifurcation from a limit cycle, direct bifurcation from a stable origin and direct bifurcation from other and more familiar robust heteroclinic cycles.
Preprint version of an article published in International Journal of Bifurcation and Chaos, 15, 9, 2005, pp. 2819-2832. DOI: 10.1142/S0218127405013708 © copyright World Scientific Publishing Company. http://www.worldscinet.com/ijbc/ijbc.shtml
15 (9), pp. 2819-2832