Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria

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Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria

Please use this identifier to cite or link to this item: http://hdl.handle.net/10036/22375

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Title: Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria
Author: Hawker, David
Ashwin, Peter
Citation: 15 (9), pp. 2819-2832
Publisher: World Scientific Publishing Company
Journal: International Journal of Bifurcation and Chaos
Date Issued: 2005
URI: http://hdl.handle.net/10036/22375
DOI: 10.1142/S0218127405013708
Links: http://dx.doi.org/10.1142/S0218127405013708
Abstract: 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.
Type: ArticlePreprint
Description: 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
Keywords: heteroclinic cyclesrobustbifurcationstabilitysymmetry
ISSN: 0218-1274


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