Abundance of strange attractors near an attracting periodically-perturbed network

TL;DR

This paper investigates the dynamics of a periodically-forced May-Leonard system, revealing the prevalence of strange attractors with stochastic properties under certain conditions, and analyzing bifurcations leading to chaos.

Contribution

It extends previous work by proving the existence of strange attractors with SRB measures in the forced system, especially for large attraction strength and near-zero forcing frequency.

Findings

Presence of strange attractors with stochastic properties for a positive measure of forcing amplitudes.

Identification of bifurcations from two-torus to rank-one strange attractors.

Confirmation of observable chaos in the system through theoretical analysis.

Abstract

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 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.