Journal of Nonlinear Science

, Volume 7, Issue 2, pp 129–176

Robust heteroclinic cycles

  • M. Krupa

DOI: 10.1007/BF02677976

Cite this article as:
Krupa, M. J Nonlinear Sci (1997) 7: 129. doi:10.1007/BF02677976


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 cyclesrobustsymmetrystabilitybifurcationsimulationexperiment

MSC numbers


Copyright information

© Springer-Verlag New York Inc 1997

Authors and Affiliations

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