Persistence and extinction of a stochastic delay Logistic equation under regime switching

被引：23

作者：

Liu, Meng ^{[1
,2
]}

Li, Wenxue ^{[1
]}

Wang, Ke ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China

[2] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2013年 / 26卷 / 01期

关键词：

Logistic equation; Markov switching; Delay; Persistence; Extinction; POPULATION-DYNAMICS; MODELS; ATTRACTIVITY; STABILITY; SYSTEMS;

D O I：

10.1016/j.aml.2012.04.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A stochastic delay Logistic equation under regime switching is proposed and studied. Sufficient conditions for extinction, non-persistence in the mean and weak persistence of the solutions are established. The critical value between weak persistence and extinction is obtained. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：140 / 144

页数：5

共 12 条

[1] PERIODIC-SOLUTIONS OF SINGLE-SPECIES MODELS WITH PERIODIC DELAY
FREEDMAN, HI
WU, JH
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1992, 23 (03) : 689 - 701
[2] PERSISTENCE IN POPULATION-MODELS WITH DEMOGRAPHIC FLUCTUATIONS
HALLAM, TG
ZHIEN, M
[J]. JOURNAL OF MATHEMATICAL BIOLOGY, 1986, 24 (03) : 327 - 339
[3] Persistence, attractivity, and delay in facultative mutualism
He, XZ
Gopalsamy, K
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 215 (01) : 154 - 173
[4] STABILITY OF PREDATION ECOSYSTEM MODELS
JEFFRIES, C
[J]. ECOLOGY, 1976, 57 (06) : 1321 - 1325
[5] GLOBAL STABILITY FOR INFINITE DELAY LOTKA-VOLTERRA TYPE SYSTEMS
KUANG, Y
SMITH, HL
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 103 (02) : 221 - 246
[6] Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching
Li, Xiaoyue
Gray, Alison
Jiang, Daqing
Mao, Xuerong
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 376 (01) : 11 - 28
[7] Global attractivity in nonautonomous logistic equations with delay
Lisena, Benedetta
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (01) : 53 - 63
[8] Persistence and extinction in stochastic non-autonomous logistic systems
Liu, Meng
Wang, Ke
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 375 (02) : 443 - 457
[9] Stochastic population dynamics under regime switching II
Luo, Qi
Mao, Xuerong
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 355 (02) : 577 - 593
[10] Mao X., 2006, STOCHASTIC DIFFERENT, DOI [10.1142/p473, DOI 10.1142/P473]

← 1 2 →