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Stochastic Analysis and Applications Volume 38, 2020 - Issue 4
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Articles

Dynamical behavior of a stochastic predator-prey model with stage structure for prey

Qun LiuSchool of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, Jilin Province, P.R. China; View further author information
,
Daqing JiangKey Laboratory of Unconventional Oil and Gas Development, China University of Petroleum (East China), Ministry of Education, Qingdao, P.R. China; Correspondence[email protected]
View further author information
,
Tasawar HayatNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi ArabiaView further author information
,
Ahmed AlsaediNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi ArabiaView further author information
&
Bashir AhmadNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi ArabiaView further author information
Pages 647-667 | Received 22 Aug 2019, Accepted 24 Dec 2019, Published online: 06 Jan 2020
 
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Abstract

In the present paper, we focus on a stochastic predator-prey model with stage structure for prey. Firstly, by using the stochastic Lyapunov function method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases. Some examples and numerical simulations are carried out to validate our analytical findings.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No.11871473) and Shandong Provincial Natural Science Foundation (No.ZR2019MA010).

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