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

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.