Optimal Harvesting of Prey in Three Species Ecological Model with a Time Delay on Prey and Predator

This paper deals with the stability analysis of three species Ecological model consists of a Prey (N₁), a predator (N₂) and a competitor (N₃) .The competitor (N₃) is competing with the Predator Species (N₂) and neutral with the prey (N₁). In this model the third species is competing with the predator for food other than the prey (N₁).In addition to that, the death rates, carrying capacities of all three species are also considered , a delay in the interaction between the prey and the predator (gestation period of the predator) and harvesting effort of prey population is also considered. The model is characterized by a couple of integro- differential equations. All the eight equilibrium points of the model are identified and their local stability is discussed for interior equilibrium point. The global stability is studied by constructing a suitable Lyapunov’s function. Suitable parameter are identified for Numerical simulation which shows that this continuous time delay model exhibits rich dynamics and time delay can further stabilize or destabilize the system.