Nonlinear Science

  • Yoshida Z
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Abstract

One phenomenon in the dynamics of differential equations which does not typically occur in systems without symmetry is heteroclinic cycles. In symmetric sys- tems, 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.

Author-supplied keywords

  • 34a34
  • 34a50
  • 58f99
  • 65l06
  • 93c15
  • aims subject classifications
  • algorithm
  • differential equation flow
  • frozen coefficients
  • lie algebra
  • manifold
  • numerical integration
  • symbolic computation

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Authors

  • Zensho Yoshida

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