Dynamical Behaviour of a Two Prey and One Predator System

• DOI: 10.1007/s12591-012-0158-y
• Publication Date: 2013-01-12T06:44:40Z
• Authors: Swarnali Sharma; G. P. Samanta
• Keywords: 0301 basic medicine; 03 medical and health sciences; 8. Economic growth

In this paper we have developed a two prey one predator population model. The interaction between first prey and predator is assumed to be governed by a Holling type II functional response where the handling time of predator for second prey is also involved. A Lotka–Volterra functional response in taken to represent the interaction between second prey and predator. Next we have studied the positivity of the solutions of the system and analyzed the existence of various equilibrium points and stability of the system at those equilibrium points. We have observed that the system is unstable at trivial equilibrium $$E_{0}$$ and the axial equilibrium $$E_{1}.$$ Next we obtain the necessary and sufficient conditions for the existence of interior equilibrium point $$E^{*}$$ and local and global stability of the system at that interior equilibrium $$E^{*}.$$ Next we have discussed about the stability of delayed model. Our analytical findings are illustrated through computer simulation, from which we have observed that the ratio of predator handling times for the second prey and the first prey ( $$\alpha $$ ) plays a key role in the stability of the system. Biological implications of our analytical findings are addressed critically.