Awakened oscillations in coupled consumer-resource pairs

TL;DR

This paper analyzes coupled consumer-resource pairs with different time scales, revealing that weak coupling induces self-sustained oscillations, applicable to biological and laser systems, through phase plane analysis of fast and slow variables.

Contribution

It introduces a novel analysis of coupled consumer-resource systems with distinct time scales, demonstrating oscillation emergence due to weak coupling.

Findings

Weak coupling induces sustained relaxation oscillations.

The model applies to biological populations and laser systems.

Oscillation periods can exceed intrinsic relaxation times.

Abstract

The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables respectively and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted). When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses.