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

The determination of asymptotic and periodic behavior of dynamic systems arising in control system analysis Final report

Asymptotic and periodic behavior prediction for nonlinear control system with mathematical model of rigid body vehicl

Two-Way Feedback Interaction between the Thermohaline and Wind-Driven Circulations

The thermohaline circulation (THC) affects the meridional atmospheric temperature gradient and therefore the atmospheric wind and the wind-driven ocean circulation. The wind-driven circulation (WDC), in turn, affects the THC by the advection of salinity anomalies into deep-water formation sites. This paper considers this two-way coupling between the WDC and THC using a simple box-type model and analysis tools from engineering feedback control. The two-way feedback can have a significant effect on the dynamics of the coupled system. For a reasonable choice of parameters, the feedback destabilizes the THC equilibrium for low freshwater forcing. For higher freshwater forcing, the feedback results in a new stable equilibrium instead of the large amplitude oscillation that develops without feedback. It is expected that the analysis approach used here may be broadly applicable to the study of feedback interconnections of other climate systems as well