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Entropy 2019, 21(3), 252; https://doi.org/10.3390/e21030252

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

School of Science, Beijing Jiaotong University, Beijing 100044, China
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Received: 10 December 2018 / Revised: 16 February 2019 / Accepted: 4 March 2019 / Published: 6 March 2019
(This article belongs to the Special Issue Biological Statistical Mechanics)
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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. View Full-Text
Keywords: predator–prey system; stochastically ultimate boundedness; stochastic extinction; Brownian motion; Crowley–Martin functional response predator–prey system; stochastically ultimate boundedness; stochastic extinction; Brownian motion; Crowley–Martin functional response
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Xu, C.; Ren, G.; Yu, Y. Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response. Entropy 2019, 21, 252.

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