Synchronization and Stability in Noisy Population Dynamics

TL;DR

This paper investigates how noise affects the stability and synchronization of predator-prey populations across multiple patches, revealing that increasing patches enhances both stability and synchrony, with residual asynchrony persisting even in large systems.

Contribution

It demonstrates that stabilization through asynchrony is a robust mechanism applicable to noisy population dynamics with multiple patches.

Findings

Increasing patches enhances stability and synchronization.

Residual asynchrony persists even with infinitely many patches.

Stabilization by asynchrony is more general than previously thought.

Abstract

We study the stability and synchronization of predator-prey populations subjected to noise. The system is described by patches of local populations coupled by migration and predation over a neighborhood. When a single patch is considered, random perturbations tend to destabilize the populations, leading to extinction. If the number of patches is small, stabilization in the presence of noise is maintained at the expense of synchronization. As the number of patches increases, both the stability and the synchrony among patches increase. However, a residual asynchrony, large compared with the noise amplitude, seems to persist even in the limit of infinite number of patches. Therefore, the mechanism of stabilization by asynchrony recently proposed by R. Abta et. al., combining noise, diffusion and nonlinearities, seems to be more general than first proposed.