Classification of robust heteroclinic cycles for vector fields in R3 with symmetry
Hawker, David; Ashwin, Peter
Date: 14 September 2005
Journal
Journal of Physics A: Mathematical and General
Publisher
Institute of Physics
Publisher DOI
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. ...
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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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