Prey and Predator Model A Study of the Transition from the Deterministic Model to the Stochastic Counterpart

Abstract

In this paper, a deterministic model was proposed and analyzed that describes the interaction between two objects representing the prey and the predator. The focus was on studying the stability of this model by determining the states that the system could be in. In addition, numerical simulations were used to clarify the behavior of the system. Converting the deterministic model to a stochastic model, is a main goal of this study, to explore and analysis the random interactions between prey and predator. The aim of this transformation was to understand the more complex dynamics that may appear in real environmental systems. Numerical simulations by MATLAB tools, were also used to illustrate the solutions behavior of the system both in its deterministic and stochastic situations.