论文标题
在一个吸引人的周期性扰动网络附近的奇怪吸引子
Abundance of strange attractors near an attracting periodically-perturbed network
论文作者
论文摘要
我们研究了周期性的May-Leonard系统的动力学。我们在场上扩展了先前的结果，并根据网络的吸引力$δ$以及周期性强迫的频率$ω$确定不同的动态状态。我们将注意力集中在$δ\ gg1 $和$ω\大约0 $的情况下，我们表明，对于积极的Lebesgue测量参数集（定期强迫的振幅），动态由具有完全随机的属性的奇怪吸引者主导，并支持Sinai-Ruelle-Bowen（SRB）。证明是通过使用王和年轻的一号奇怪吸引者理论来执行的。这项工作结束了关于在这种情况下可观察到的可持续混乱存在的讨论。我们还确定了一些从吸引人的两道齿到排名一的奇怪吸引子的过渡中发生的一些分叉，这些吸引子的存在是通过数值模拟提出的。
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 $δ$ of the network and the frequency $ω$ of the periodic forcing. We focus our attention in the case $δ\gg1$ and $ω\approx 0$, 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 a Sinai-Ruelle-Bowen (SRB) measure. The proof is performed by using the Wang and Young 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.
