Awakened oscillations in coupled consumer-resource pairs

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. copyright © 2014 almaz mustafin.