Robust heteroclinic cycles |
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Authors: | M Krupa |
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Institution: | (1) Institut für Angewandte und Numerische Mathematik, TU Wien, Wiedner Hauptstrasse 8–10/115/1, A-1040 Wien, Austria |
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Abstract: | Summary 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. |
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Keywords: | heteroclinic cycles robust symmetry stability bifurcation simulation experiment |
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