Dynamics of a linearly-perturbed May-Leonard competition model

The May-Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this talk, we will discuss an extended May-Leonard model, where the system is perturbed by adding the capability of global mutations, allowing one species to evolve to the other two in a linear manner. Our focus will be on investigating the ensuing dynamics upon perturbation, highlighting the ways in which the behavior of the system is retained as well as surveying the changes that arise. Notable changes include a richer variety of steady states, leading to more varied options of coexistence, in addition to an extended parameter space where limit cycles occur. Indeed, a linear perturbation proves to be significant enough to substantially influence the dynamics of the extended model, even with small mutation rates.