Modeling Spatial Synchronization of Predator-Prey Oscillations via the XY Model under Demographic Stochasticity and Migration

TL;DR

This paper explores how demographic noise and migration influence spatial synchronization in predator-prey systems, using stochastic simulations and analytical models to understand phase transitions and ecological resilience.

Contribution

It introduces a novel combination of stochastic simulations and XY model-inspired analysis to study ecological synchronization under demographic stochasticity and dispersal.

Findings

Demographic noise significantly affects synchronization patterns.

Migration influences phase transition thresholds.

Theoretical framework links ecological dynamics with statistical physics models.

Abstract

We investigate stochastic predator-prey dynamics and their spatial phase synchronization using the Rosenzweig-MacArthur model coupled across multiple patches. Combining stochastic simulations based on the Gillespie algorithm with analytical methods inspired by the XY model, we uncover fundamental mechanisms through which demographic noise and dispersal shape synchronization and phase transitions. This study offers a theoretical foundation for understanding and managing large-scale ecological synchrony and ecosystem resilience.