Chaotic behavior of three competing species of May-Leonard model under small periodic perturbations

The influence of periodic perturbations to a Lotka-Volterra system, modeling a competition between three species, is studied, provided that in the unperturbed case the system has a unique attractor - a contour of heteroclinic orbits joining unstable equilibria. It is shown that the perturbed system may manifest regular behavior corresponding to the existence of a smooth invariant torus, and, as well, may have chaotic regimes depending on some parameters. Theoretical results are confirmed by numerical simulations.