Journal of Nonlinear Science

, Volume 7, Issue 2, pp 129–176

Robust heteroclinic cycles

  • M. Krupa


One phenomenon in the dynamics of differential equations which does not typically occur in systems without symmetry is heteroclinic cycles. In symmetric systems, cycles can be robust for symmetry-preserving perturbations and stable. Cycles have been observed in a number of simulations and experiments, for example in rotating convection between two plates and for turbulent flows in a boundary layer. Theoretically the existence of robust cycles has been proved in the unfoldings of some low codimension bifurcations and in the context of forced symmetry breaking from a larger to a smaller symmetry group. In this article we review the theoretical and the applied research on robust cycles.

Key words

heteroclinic cycles robust symmetry stability bifurcation simulation experiment 

MSC numbers

58F12 58F14 34-02 34C37 


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Copyright information

© Springer-Verlag New York Inc 1997

Authors and Affiliations

  • M. Krupa
    • 1
  1. 1.Institut für Angewandte und Numerische MathematikTU WienWienAustria

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