Dynamics of a Stochastic Predator–Prey Model with Stage Structure for Predator and Holling Type II Functional Response

被引：1
作者：
Qun Liu
Daqing Jiang
Tasawar Hayat
Ahmed Alsaedi
机构：
[1] Northeast Normal University,School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE
[2] Yulin Normal University,School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing
[3] King Abdulaziz University,Nonlinear Analysis and Applied Mathematics (NAAM)
[4] China University of Petroleum,Research Group
[5] Quaid-i-Azam University,College of Science
来源：
Journal of Nonlinear Science | 2018年 / 28卷
关键词：
Predator–prey model; Stage structure; Holling type II functional response; Stationary distribution; Ergodicity; Extinction; 34E10; 60H10; 92B05; 92D25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we develop and study a stochastic predator–prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.
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页码：1151 / 1187
页数：36
相关论文
共 68 条
[1]  
Al-Omari JFM(2015)The effect of state dependent delay on harvesting on a stage-structured predator–prey model Appl. Math. Comput. 271 142-153
[2]  
Beddington JR(1977)Harvesting natural populations in a randomly fluctuating environment Science 197 463-465
[3]  
May RM(2008)Growth and extinction of populations in randomly varying environments Comput. Math. Appl. 56 631-644
[4]  
Braumann CA(2014)Hopf bifurcation analysis for a ratio-dependent predator–prey system with two delays and stage structure for the predator Appl. Math. Comput. 231 214-230
[5]  
Deng L(1991)Persistence and global asymptotic stability of single species dispersal models with stage structure Q. Appl. Math. 49 351-371
[6]  
Wang X(1984)Persistence in stochastic food web models Bull. Math. Biol. 46 357-370
[7]  
Peng M(1986)Stability for multispecies population models in random environments Nonlinear Anal. 10 1411-1419
[8]  
Freeman HI(2006)Global dynamics of a predator–prey model with stage structure for predator SIAM J. Appl. Math. 67 1379-1395
[9]  
Wu J(2006)Global stability for a stage-structured predator–prey model Math. Sci. Res. J. 10 214-226
[10]  
Gard TC(2010)A Lyapunov functional for a stage-structured predator–prey model with nonlinear predation rate Nonlinear Anal. Real World Appl. 11 3653-3665
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