Behavioural analysis of two prey-two predator model

Abstract

To deal with real-life diversity of our ecosystem, this paper analyzes two prey-two predator model including both Type-I and Type-II functional responses. The interior equilibrium point of the proposed model is calculated; and behaviour of the model around that point is studied. Local stability at an interior equilibrium point is discussed; and possibility of Hopf-bifurcation with probable direction is studied. A generalized form of the Poincaré-Bendixon criterion is applied to establish the sufficient conditions for global stability of the proposed model surrounding at an interior equilibrium point. Numerical simulations are also conducted in support of our work. Conclusions of our findings and some probable future directions are also included at the end.