ON THE STABILITY OF AGE SPECIFIC PREY AND PREDATORS SYSTEM WITH TWO FUNC-TIONAL RESPONSES

Abstract

In this paper, a mathematical model is proposed to describe and analyse the dynamics of two age specific prey and one predator system. The dynamics of a prey- predator system, where prey population has two stages juvenile and adult with adult prey having anti-predator behaviour modelled by a system of autonomous ordinary differential equations. The main feature of the model is that two different functional response of the predator are incorporated in the model to represent the difference in the way the predator feeds on each of the prey species. Juvenile prey (which is considered as weak) is the easy to capture prey and the predator’s re-sponse to the juvenile prey is Holling type II. The adult prey (which is considered as strong) having anti predator behav-iour is hard to capture and this behaviour is represented by the ratio-dependent response of the predator. Interspecific competition among the prey species is included in the mod-el. In the absence of the predator logistic growth of the prey population are also included in the prey equations. Thus the model presented here is a three variable model with Juvenile prey population, adult prey population and one predator population. Existence of equilibria, their nature is analysed. The stability criteria of the equilibria and conditions for sta-bility are also analysed.