Heteroclinic Cycles of A Symmetric May-Leonard Competition Model with Seasonal Succession

TL;DR

This paper analyzes the stability of heteroclinic cycles in a symmetric May-Leonard competition model with seasonal changes, revealing rich dynamics and bifurcations through theoretical and numerical methods.

Contribution

It provides explicit stability conditions, an expression for the carrying simplex, and explores bifurcations and complex dynamics introduced by seasonal succession.

Findings

Derived stability conditions for heteroclinic cycles.

Explicit expression of the carrying simplex in a special case.

Identified rich dynamics including periodic solutions and invariant curves.

Abstract

In this paper, we are concerned with the stability of heteroclinic cycles of the symmetric May-Leonard competition model with seasonal succession. Sufficient conditions for stability of heteroclinic cycles are obtained. Meanwhile, we present the explicit expression of the carrying simplex in a special case. By taking \phi as the switching strategy parameter for a given example, the bifurcation of stability of the heteroclinic cycle is investigated. We also find that there are rich dynamics (including nontrivial periodic solutions, invariant closed curves and heteroclinic cycles) for such a new system via numerical simulation. Biologically, the result is interesting as a caricature of the complexities that seasonal succession can introduce into the classical May-Leonard competitive model.