relaxation oscillations

In this article we consider simulation of appearance oscillations in abundance of biological species and concomitant abrupt changes in the population development process. The inductors for the appearance of many long-period fluctuations, such as herring cycles in the Pacific Ocean, have not yet been fully established. Changes in population cycles can take extreme nature and violate prevailing uniformity of biological diversity, even evoke significant impacts on ecosystems.

In the work the mathematical model of the thalamocortical network’s unit cell and it’s characteristic dynamical modes in system, describing the interaction between a thalamus, thalamus reticular nucleus and a cortex, is studied.

A model for competition of two different species is considered. It is assumed that each consumer specializes on one resource only. The resource uptake rates are held constant.The basic feature of the model is that the dynamics of the resource is much slower than that of the consumer.The two consumers are coupled through direct reciprocal inhibition. Besides, self-limitation of the consumers due to overcrowding is also taken into account. The resources are noninteractive.