Stability of oscillations in the spatially extended May-Leonard model

TL;DR

This paper investigates the stability of oscillatory solutions in a spatially extended May-Leonard model, revealing conditions for stability, longwave instabilities, and a period doubling transition affecting spatial uniformity.

Contribution

It provides exact time-periodic solutions for the extended May-Leonard model and analyzes their stability against spatial disturbances, including longwave and period doubling instabilities.

Findings

Stability of oscillations depends on spatial disturbance characteristics.

Longwave spatial modulations can destabilize solutions.

A period doubling instability leads to loss of spatial uniformity.

Abstract

The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their stability with respect to spatially periodic disturbances is studied. The stability of solu tions with respect to longwave spatial modulations is revealed. A period doubling instability breaking the spatial uniformity is found.