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

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      Date
      2005
      Author
      Hawker, David
      Ashwin, Peter
      Department
      University of Exeter
      Date issued
      2005
      Journal
      Journal of Physics A: Mathematical and General
      Type
      Article
      Language
      en
      Publisher
      Institute of Physics
      Links
      http://dx.doi.org/10.1088/0305-4470/38/39/002
      http://www.iop.org/EJ/abstract/0305-4470/38/39/002
      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.
      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
      Citation
      38 (39), pp. 8319-8335
      DOI
      https://doi.org/10.1088/0305-4470/38/39/002
      URI
      http://hdl.handle.net/10036/22992
      ISSN
      0305-4470
      1361-6447
      Collections
      • Mathematics
      • Centre for Systems, Dynamics and Control

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