A stochastic prey-predator model with time-dependent delays

被引：3
作者：
Dai, Xiangjun [1 ]
Mao, Zhi [1 ]
Li, Xiaojun [1 ]
机构：
[1] TongRen Univ, Sch Data Sci, Tongren 554300, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2017年
关键词：
prey-predator system; time-dependent delays; stochastically ultimate bounded; persistence; extinction; RANDOM PERTURBATION; LOGISTIC EQUATION; COMPETITIVE MODEL; GLOBAL STABILITY; PERSISTENCE; EXTINCTION; DIFFUSION; SYSTEMS;
D O I：
10.1186/s13662-017-1321-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A stochastic predator-prey system with time-dependent delays is considered. Firstly, we show the existence of a global positive solution and stochastically ultimate boundedness. Secondly, the critical value between weak persistence and extinction of the prey is obtained and we also give the asymptotic pathwise estimation. Finally, we simulate the model to illustrate our results.
引用
收藏
页数：15
相关论文
共 27 条
[1]   On a delay population model with a quadratic nonlinearity without positive steady state [J].
Bastinec, Jaromir ;
Berezansky, Leonid ;
Diblik, Josef ;
Smarda, Zdenek .
APPLIED MATHEMATICS AND COMPUTATION, 2014, 227 :622-629
[2]   On a delay population model with quadratic nonlinearity [J].
Berezansky, Leonid ;
Bastinec, Jaromir ;
Diblik, Josef ;
Smarda, Zdenek .
ADVANCES IN DIFFERENCE EQUATIONS, 2012,
[3]   A stochastic predator-prey model with delays [J].
Du, Bo ;
Wang, Yamin ;
Lian, Xiuguo .
ADVANCES IN DIFFERENCE EQUATIONS, 2015, :1-16
[4]   PERSISTENCE IN MODELS OF 3 INTERACTING PREDATOR-PREY POPULATIONS [J].
FREEDMAN, HI ;
WALTMAN, P .
MATHEMATICAL BIOSCIENCES, 1984, 68 (02) :213-231
[5]  
Freedman HI., 1980, DETERMINISTIC MATH M
[6]  
Gard T. C., 1988, INTRO STOCHASTIC DIF
[7]   PERSISTENCE IN STOCHASTIC FOOD WEB MODELS [J].
GARD, TC .
BULLETIN OF MATHEMATICAL BIOLOGY, 1984, 46 (03) :357-370
[8]   An algorithmic introduction to numerical simulation of stochastic differential equations [J].
Higham, DJ .
SIAM REVIEW, 2001, 43 (03) :525-546
[9]   Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation [J].
Jiang, Daqing ;
Shi, Ningzhong ;
Li, Xiaoyue .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 340 (01) :588-597
[10]  
Kuang Y., 1993, Delay Differential Equations with Applications in Population Dynamics
123