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

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 ϕ 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.