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Two-parameter locus of boundary crisis: mind the gaps!

Research output: Working paperWorking paper and Preprints

  • Hinke M Osinga
  • J Rankin
Original languageEnglish
StatePublished - Jul 2010


Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of boundary crisis is associated with curves of homo- or heteroclinic tangency bifurcations of saddle periodic orbits. It is known that the locus of boundary crisis contains many gaps, corresponding to channels (regions of positive measure) where a non-chaotic attractor persists. One side of such a subduction channel is a saddle-node bifurcation of a periodic orbit that marks the start of a periodic window in the chaotic regime; the other side of the channel is formed by a homo- or heteroclinic tangency bifurcation associated with this diffferent saddle periodic orbit. We present a two-parameter study of boundary crisis in the Ikeda map, which models the dynamics of energy levels in a laser ring cavity. We confirm the existence of many gaps on the boundary-crisis locus. However, the gaps correspond to subduction channels that can have a rather different structure compared to what is known in the literature.

Additional information

Sponsorship: The research of HMO was supported by an Advanced Research Fellowship from the Engineering and Physical Sciences Research Council. The research of JR was supported by the Natural Environment Research Council.

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    Submitted manuscript, 537 KB, PDF-document


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