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2014 Awakened Oscillations in Coupled Consumer-Resource Pairs
Almaz Mustafin
J. Appl. Math. 2014: 1-20 (2014). DOI: 10.1155/2014/561958

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.

Citation

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Almaz Mustafin. "Awakened Oscillations in Coupled Consumer-Resource Pairs." J. Appl. Math. 2014 1 - 20, 2014. https://doi.org/10.1155/2014/561958

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131688
MathSciNet: MR3261254
Digital Object Identifier: 10.1155/2014/561958

Rights: Copyright © 2014 Hindawi

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