Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge

In this study, we implement a Nonstandard Finite Difference (NSFD) scheme for a predator-prey model involving cannibalism and refuge in predator. The scheme which is considered as a discrete dynamical system is analyzed. The performed analysis includes the determination of equilibrium point and its local stability. The system has four equilibrium points, namely the origin, the prey extinction point, the predator extinction point, and the coexistence point, which have exactly the same form and existence conditions as those in continuous system. The local stability of each first three equilibrium points is consistent with the one in continuous system. The stability of the coexistence point depends on the integration time step size. Nevertheless, the NSFD scheme allows us to choose the integration time step size for the solution to converge to a feasible point more flexible than the Euler and 4th order Runge-Kutta schemes. These are shown via numerical simulations.