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

Supply chain modeled as a metabolic pathway

A new model of economic production process is proposed (in the form of a set of ODEs) based on an idea that nonconsumable factors of production facilitate the conversion of inputs to output in much the same catalytic way as do enzymes in living cells when transforming substrates into different chemical compounds. The output of a converging, multi-resource, single-product supply chain network is shown to depend on the minimum of its inputs in the form of the Leontief--Liebig production function, providing the validity of the clearing function approximation. In turn use of the clearing function is legitimate when the machine processing time is much shorter than the machine loading time

A biologically inspired fluid model of the cyclic service system

A deterministic fluid model in the form of nonlinear ordinary differential equations is developed to provide the description for a multichannel service system with service-in-random-order queue discipline, abandonment and re-entry, where servers are treated like enzyme molecules. The parametric analysis of the model’s fixed point is given, particularly, how the arrival rate of new customers affects the steady-state demand. It is also shown that the model implies a saturating clearing function (yield vs. demand) of the Karmarkar type providing the mean service time is much shorter than the characteristic waiting time