Synchronization of coupled demographic oscillators

TL;DR

This paper demonstrates how coupled demographic oscillators, modeled through predator-prey systems, can synchronize their frequencies as coupling strength increases, with theoretical predictions confirmed by simulations.

Contribution

It introduces a novel analysis of synchronization in demographic oscillators using van Kampen expansion and phase dynamics, revealing frequency entrainment phenomena.

Findings

Synchronization occurs at high coupling strength.

Power spectra show single peak at large coupling.

Phase difference stabilizes with increasing coupling.

Abstract

Demographic oscillators are individual-based systems exhibiting temporal cycles sustained by the stochastic dynamics of the microscopic interacting particles. We here use the example of coupled predator-prey oscillators to show that synchronization to a common frequency can occur between two such systems, even if they oscillate at different frequencies in the absence of coupling. The power spectra of the separate and the coupled systems are computed within a van Kampen expansion in the inverse system size, and it is found that they exhibit two peaks at separate frequencies at low coupling, but that only one peak is present at large enough coupling strength. We further make predictions on the time behaviour of the phases of the two oscillators, and their phase difference, and confirm the frequency entrainment at sufficiently large coupling. Theoretical results are verified convincingly in numerical simulations.