Classification of robust heteroclinic cycles for vector fields in R3 with symmetry

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Classification of robust heteroclinic cycles for vector fields in R3 with symmetry

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dc.contributor.author Hawker, David en_GB
dc.contributor.author Ashwin, Peter en_GB
dc.contributor.department University of Exeter en_GB
dc.date.accessioned 2008-04-11T08:40:34Z en_GB
dc.date.accessioned 2011-01-25T10:33:20Z en_US
dc.date.accessioned 2013-03-20T12:29:09Z
dc.date.issued 2005 en_GB
dc.description.abstract We consider a classification of robust heteroclinic cycles in the positive octant of R3 under the action of the symmetry group (Z2)3. We introduce a coding system to represent different classes up to a topological equivalence, and produce a characterization of all types of robust heteroclinic cycle that can arise in this situation. These cycles may or may not contain the origin within the cycle. We proceed to find a connection between our problem and meandric numbers. We find a direct correlation between the number of classes of robust heteroclinic cycle that do not include the origin and the 'Mercedes-Benz' sequence of integers characterizing meanders through a 'Y-shaped' configuration. We investigate upper and lower bounds for the number of classes possible for robust cycles between n equilibria, one of which may be the origin. en_GB
dc.identifier.citation 38 (39), pp. 8319-8335 en_GB
dc.identifier.doi 10.1088/0305-4470/38/39/002 en_GB
dc.identifier.uri http://hdl.handle.net/10036/22992 en_GB
dc.language.iso en en_GB
dc.publisher Institute of Physics en_GB
dc.relation.url http://dx.doi.org/10.1088/0305-4470/38/39/002 en_GB
dc.relation.url http://www.iop.org/EJ/abstract/0305-4470/38/39/002 en_GB
dc.title Classification of robust heteroclinic cycles for vector fields in R3 with symmetry en_GB
dc.type Article en_GB
dc.type Preprint en_GB
dc.date.available 2008-04-11T08:40:34Z en_GB
dc.date.available 2011-01-25T10:33:20Z en_US
dc.date.available 2013-03-20T12:29:09Z
dc.identifier.issn 0305-4470 en_GB
dc.identifier.issn 1361-6447 en_GB
dc.description Copyright © 2005 IOP Publishing Ltd. This is the pre-print version of an article subsequently published in Journal of Physics A: Mathematical and General Vol. 38 (39), pp. 8319-8335, DOI:10.1088/0305-4470/38/39/002 en_GB
dc.identifier.journal Journal of Physics A: Mathematical and General en_GB


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