Incorporating the influence of hunting cooperation and competition into the prey-predator model

Abstract

This mathematical model consists of three nonlinear ordinary differential equations between two prey (N1, N2) and only one predator (P). The two prey (N1, N2) grow logistically under predator pressure, and the predator depends mainly on the first prey (N1). According to function response Holling’s type II formula, indirect competition exists between N1 and N2 because the predator exerts strong pressure on first prey (N1), while second prey (N2) is affected more simply. Equilibrium points for the mathematical model between predator and two prey, which stabilize over time, were calculated, and the local stability around the equilibrium points of this proposed model was analyzed using the Lyapunov function. Finally, numerical simulation was used to demonstrate the results.