Euler Scheme for a Predator-Prey Model Incorporating Predator Cannibalism and Refuge

In this paper, we consider Euler’s discretization scheme for a predator-prey model incorporating predator cannibalism and refuge, since it is one of standard methods for solving initial value problems. The discretized system is then analyzed dynamically for its equilibrium points and their local stability. The results of this dynamical analysis are then compared to the dynamical properties of the original continuous model. It is found that the local stability properties for all of the equilibrium points, i.e. the extinction point of both prey and predator populations, the prey extinction point, the predator extinction point, and the coexistence point of the discrete system are consistent with the continuous model if time-step size are not exceed the threshold. The threshold depends on the parameters of model.