Abundance of Strange Attractors Near an Attracting Periodically Perturbed Network

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