Strange attractors in a predator–prey system with non-monotonic response function and periodic perturbation

Abstract

A system of ordinary differential equations of a predator-prey type, depending on nine parameters, is studied. We have included in this model a nonmonotonic response function and time periodic perturbation. Using numerical continuation software, we have detected three codimension two bifurcations for the unperturbed system, namely cusp, Bogdanov-Takens and Bautin bifurcations. Furthermore, we concentrate on two regions in the parameter space, the region where the Bogdanov-Takens and the region where Bautin bifurcations occur. As we turn on the time perturbation, we find strange attractors in the neighborhood of invariant tori of the unperturbed system.2010 Mathematics Subject Classification. 37C60, 37G15, 34A34, 92D25.

Preface Special issue in honor of Reinout Quispel

“…There are three papers on continuous dynamical systems, all related to predator-prey equations. Tuwankotta and Harjanto [32] consider a family of classical planar predator-prey systems, finding that a small periodic perturbation induces strange attractors in a neighbourhood of an invariant torus of the unperturbed system. Christodoulidi, Hone, and Kouloukas [6] find new, highdimensional integrable and superintegrable cases of Lotka-Volterra systems, and numerical evidence for chaos in other cases.…”