SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 541-570, January 2021.
We study the dynamics of the periodically forced May--Leonard system. We extend previous results on the field, and we identify different dynamical regimes depending on the strength of attraction $\delta$ of the network and the frequency $\omega$ of the periodic forcing. We focus our attention in the case $\delta\gg1$ and $\omega \approx 0$, where we show that, for a positive Lebesgue measure set of parameters (amplitude of the periodic forcing), the dynamics are dominated by strange attractors with fully stochastic properties, supporting Sinai--Ruelle--Bowen (SRB) measures. The proof is performed by using the Wang and Young's theory of rank-one strange attractors. This work ends the discussion about the existence of observable and sustainable chaos in this scenario. We also identify some bifurcations occurring in the transition from an attracting two-torus to rank-one strange attractors, whose existence has been suggested by numerical simulations.

中文翻译：

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吸引周期性扰动网络附近的奇异吸引子的数量

SIAM应用动力系统杂志，第20卷，第1期，第541-570页，2021年1月。
我们研究了周期性强迫May-Leonard系统的动力学。我们扩展了该领域的先前结果，并根据网络的吸引力$ \ delta $和周期性强迫的频率$ \ omega $来确定不同的动力机制。我们将注意力集中在$ \ delta \ gg1 $和$ \ omega \ approx 0 $的情况下，其中我们表明，对于正的Lebesgue量度参数集（周期性强迫的振幅），动力学由奇怪的吸引子控制具有完全随机属性，支持西奈-鲁伊尔-博文（SRB）措施。证明是通过使用Wang和Young的排名第一的奇异吸引子理论进行的。这项工作结束了在这种情况下有关可观察到的和可持续的混乱的存在的讨论。