Stability of a stochastic logistic model with distributed delay

被引：21
|
作者：
Liu, Meng [1 ,2 ]
Wang, Ke [2 ]
Hong, Qiu [2 ]
机构：
[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Peoples R China
[2] Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China
来源：
MATHEMATICAL AND COMPUTER MODELLING | 2013年 / 57卷 / 5-6期
关键词：
Logistic equation; Random perturbations; Distributed delay; Global stability; ASYMPTOTIC PROPERTIES; RANDOM-ENVIRONMENTS; GLOBAL STABILITY; POPULATION-MODEL; INFINITE DELAY; EQUATIONS; SYSTEMS; PERTURBATION; ATTRACTIVITY; SIMULATIONS;
D O I：
10.1016/j.mcm.2012.10.006
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
This paper is concerned with the stability of the solutions to the stochastic logistic model with distributed delay, which is represented by the equation dx(t) = x(t)(1 - ax(t) - b integral(0)(-tau)x(t + theta)d mu(theta))[rdt + sigma db(t)], where B-t is a standard Brownian motion. This study shows that the above stochastic system has a global positive solution with probability 1 and establishes the sufficient conditions for stability of the zero solution and the positive equilibrium. Several numerical examples are introduced to illustrate the results. Some recent results are improved and generalized. (C) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1112 / 1121
页数：10
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