Stability in distribution of competitive Lotka-Volterra system with Markovian switching

被引：22
作者：
Hu, Guixin [1 ]
Wang, Ke [1 ,2 ]
机构：
[1] Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China
[2] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China
来源：
APPLIED MATHEMATICAL MODELLING | 2011年 / 35卷 / 07期
关键词：
Lotka-Volterra model; Stability in distribution; Markov chain; BEHAVIOR; MODEL;
D O I：
10.1016/j.apm.2010.12.025
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, we consider a stochastic Lotka-Volterra competitive system dxi(t) = x(t) {[b(i)(xi(t)) - Sigma(n)(j=1)aij(xi(t))x(j)(t)]dt + sigma(i)(xi(t)dw(i)(t)}. where w(i)(t)(i = 1,2,..., n) are independent standard Brownian motions and xi(.) is Markov chain taking values in a finite space M = {1,2, ..., m}. Global attractivity, upper boundedness and other properties are obtained. In addition, asymptotically stable in distribution as the main result of our paper is derived under some conditions. We gave a numerical simulation for invariant distribution of an example by using the Monte Carlo simulation method at the end. (C) 2010 Elsevier Inc. All rights reserved.
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收藏
页码：3189 / 3200
页数：12
相关论文
共 14 条
[1]  
Anderson W., 1991, CONTINUOUS TIME MARK, DOI 10.1007/978-1-4612-3038-0
[2]  
Barbalat I., 1959, Rev. Math. Pures Appl., V4, P267
[3]   STABILITY IN DISTRIBUTION FOR A CLASS OF SINGULAR DIFFUSIONS [J].
BASAK, GK ;
BHATTACHARYA, RN .
ANNALS OF PROBABILITY, 1992, 20 (01) :312-321
[4]  
Gard T. C., 1988, INTRO STOCHASTIC DIF
[5]  
Ikeda N., 1981, Stochastic Differential Equations and Diffusion Processes
[6]   Population dynamical behavior of Lotka-Volterra system under regime switching [J].
Li, Xiaoyue ;
Jiang, Daqing ;
Mao, Xuerong .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 232 (02) :427-448
[7]   POPULATION DYNAMICAL BEHAVIOR OF NON-AUTONOMOUS LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH RANDOM PERTURBATION [J].
Li, Xiaoyue ;
Mao, Xuerong .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 24 (02) :523-545
[8]  
Mao X., 2007, Stochastic Differential Equations and Applications, V2nd, DOI DOI 10.1533/9780857099402
[9]  
Mao X., 2006, STOCHASTIC DIFFRENTI
[10]   Asymptotic behaviour of the stochastic Lotka-Volterra model [J].
Mao, XR ;
Sabanis, S ;
Renshaw, E .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 287 (01) :141-156
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