A codimension-two resonant bifurcation from a heteroclinic cycle with complex eigenvalues |
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Authors: | Claire M Postlethwaite Jonathan H P Dawes |
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Affiliation: |
a DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, UK |
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Abstract: | Robust heteroclinic cycles between equilibria lose stability either through local bifurcations of their equilibria or through global bifurcations. This paper considers a global loss of stability termed a 'resonant' bifurcation. This bifurcation is usually associated with the birth or death of a nearby periodic orbit, and generically occurs in either a supercritical or subcritical manner. For a specific robust heteroclinic cycle between equilibria with complex eigenvalues we examine the codimension-two point that separates the supercritical and subcritical. We investigate the bifurcation structure and show the existence of further bifurcations of periodic orbits. |
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