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.