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.
CITATION STYLE
Scott, A. (2003). Nonlinear Science. Nonlinear Science. Oxford University PressOxford. https://doi.org/10.1093/oso/9780198528524.001.0001
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