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• W2018207712 abstract "Robust heteroclinic cycles (RHCs) arise naturally in collections of symmetric differential equations derived as dynamical models in many fields, including fluid mechanics, game theory and population dynamics. In this paper, we present a careful study of the complicated dynamics generated by small amplitude periodic perturbations of a stable robust heteroclinic cycle (RHC). We give a detailed derivation of the Poincaré map for trajectories near the RHC, asymptotically correct in the limit of small amplitude perturbations. This reduces the nonautonomous system in R3 to a 2D map. We identify three distinct dynamical regimes. The distinctions between these regimes depend subtly on different distinguished limits of the two small parameters in the problem. The first regime corresponds to the RHC being only weakly attracting: here we show that the system is equivalent to a damped nonlinear pendulum with a constant torque. In the second regime the periodically-perturbed RHC is more strongly attracting and the system dynamics corresponds to that of a (non-invertible or invertible) circle map. In the third regime, of yet stronger attraction, the dynamics of the return map is chaotic and no longer reducible to a one-dimensional map. This third regime has been noted previously; our analysis in this paper focusses on providing quantitative results in the first two regimes." @default.
• W2018207712 created "2016-06-24" @default.
• W2018207712 creator A5064073614 @default.
• W2018207712 creator A5078133914 @default.
• W2018207712 date "2013-11-01" @default.
• W2018207712 modified "2023-09-27" @default.
• W2018207712 title "Dynamics near a periodically-perturbed robust heteroclinic cycle" @default.
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• W2018207712 doi "https://doi.org/10.1016/j.physd.2013.07.009" @default.
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