Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response

Abstract

In this paper, we researched some dynamical behaviors of a stochastic predator–prey system, which is considered under the combination of Crowley–Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the system. Then, we studied the stochastically ultimate boundedness of the solution. Furthermore, we established two sufficient conditions, which are separately given to ensure the stochastic extinction of the prey and predator populations. In the end, we carried out the numerical simulations to explain some cases.

Keywords

• predator–prey system
• stochastically ultimate boundedness
• stochastic extinction
• Brownian motion
• Crowley–Martin functional response