Amplitude dependent frequency, desynchronization, and stabilization in noisy metapopulation dynamics

TL;DR

This paper investigates how amplitude-dependent frequency variations, combined with migration and noise, can stabilize population oscillations in ecological metapopulations, revealing a mechanism for persistent oscillatory behavior.

Contribution

It introduces a model showing that frequency dependence on amplitude, coupled with noise and migration, stabilizes oscillations in ecological systems, extending understanding beyond traditional explanations.

Findings

Frequency dependence amplifies noise effects across patches.

Migration stabilizes desynchronized oscillations near the homogeneous state.

Large noise levels can prevent extinction in unstable systems.

Abstract

The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that the combined effects of migration and noise cannot account for the stabilization. The missing ingredient is the dependence of the oscillations' frequency upon their amplitude; with that, noise-induced differences between patches are amplified due to the frequency gradient. Migration among desynchronized regions then stabilizes a "soft" limit cycle in the vicinity of the homogenous manifold. A simple model of diffusively coupled oscillators allows the derivation of quantitative results, like the functional dependence of the desynchronization upon diffusion strength and frequency differences. The oscillations' amplitude is shown to be (almost) noise independent. The results are compared with a numerical integration of the marginally stable Lotka-Volterra equations. An unstable system is extinction-prone for small noise, but stabilizes at larger noise intensity.