Stochastic dynamic behavior for the prey-predator problem with Holling-type II functional response

Abstract

The purpose of our study is to examine the stochastic stability of one of the important problems associated with ecology, namely the problem of prey and predators. This study was based on the type II functional response. After constructing the stochastic mathematical system that describes the problem, we demonstrated the system’s biological acceptability by providing the necessary conditions for the solution to be positive as well as studying the stationary distribution. By doing so, we may have studied the stability of the system. The comparison approach is often employed to determine the prerequisites for the extinction or persistence of prey. Finally, to demonstrate the results’ accuracy and realism, we present a numerical analysis of the problem in question.