Desynchronization of strongly nonlinear oscillations by coupling strengthening

TL;DR

This paper explores how coupling strength affects the synchronization of strongly nonlinear oscillations in ecological models, using stability analysis and numerical simulations to understand desynchronization phenomena.

Contribution

It establishes a link between network stability and spatial perturbations, and analyzes nonlinear oscillations in ecological networks with numerical insights.

Findings

Strong nonlinear oscillations can be desynchronized by increased coupling.

The master stability function helps predict stability of cyclic competition.

Numerical results illustrate the impact of coupling on oscillation dynamics.

Abstract

We investigate cyclic dominance models and their extensions to both network systems and reaction-diffusion frameworks. Using linear stability analysis, we establish the relationship between the stability of synchronized states in network systems and the response of homogeneous solutions subjected to spatially periodic perturbations. Furthermore, we explore the mathematical properties of networks characterized by strong nonlinear oscillations in an ecological context. Finally, we present numerical results for the master stability function of a competitive three-species Lotka-Volterra model, highlighting its role in understanding the dynamics of cyclic competition.