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.Comment: 31 pages, 8 figures 2 tables, 48 reference
