Food-Consumer Interactions: Role of Time – Varying Key Parameters – a New Perspective

Abstract

In this article, we have considered a simple food-consumer dynamic model in which the supply of food and the death of consumer species play the major role. The parameters representing these factors are allowed to vary with respect to time. It is established that by proper selection of these parameter functions, the system may be made to approach a desired state. It is noticed that these parameters define a space of equilibria for the given system in the limiting case. In case of different consumer species surviving on the same food, when there is no interference in consumption of one by the other, the growth is as desired. Growth is not as desired when one of the species is interfering with the food consumption of the other and the growth of the larger consumer is dominating. By simple variations in the death/removal of dominating species, the situation may be reversed in favor of the other species. The growth is as desired when the parameters are fixed constants. Examples are provided to understand the results and to illustrate various situations. The approach is tried on a popular mathematical model of biology to draw some useful conclusions. The study opens interesting problems for further research.