Chaotic attractors in the four-dimensional Leslie–Gower competition model

Abstract

We study the occurrence of the chaotic attractor in the four-dimensional classical Leslie-Gower competition model. We find that chaos can be generated by a cascade of quasiperioddoubling bifurcations starting from a supercritical Neimark-Sacker bifurcation of the positive fixed point in this model. The chaotic attractor is contained in the three-dimensional carrying simplex, that is a globally attracting invariant manifold. Biologically, the result implies that the invasion attempts by an invader into a trimorphic population under the Leslie-Gower dynamics can lead to chaos.

Computer‐assisted analysis of chaos in a three‐species food chain model

“…But in addition, as we know, chaos also exists widely in many ecosystems, see, for example, Refs. [12,16,21,34,35]. As shown in the literature, chaotic behaviors in these models are mainly observed and studied by numerical simulation and Lyapunov exponents.…”