Survival analysis for a periodic predator-prey model with prey impulsively unilateral diffusion in two patches

被引：13

作者：

Zhang, Long ^{[1
]}

Teng, Zhidong ^{[1
]}

Liu, Zijian ^{[2
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Univ Elect Sci & Technol China, Sch Appl Math, Chengdu 610054, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2011年 / 35卷 / 09期

关键词：

Predator-prey system; Unilateral diffusion; Impulse; Periodic solution; Extinction; GLOBAL STABILITY; POPULATION INTERACTIONS; MATHEMATICAL-MODELS; VOLTERRA MODELS; PERMANENCE; DISPERSAL; ENVIRONMENT; EXTINCTION; SYSTEMS; PERSISTENCE;

D O I：

10.1016/j.apm.2011.02.041

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we study a periodic predator-prey system with prey impulsively unilateral diffusion in two patches. Firstly, based on the results in [41], sufficient conditions on the existence, uniqueness and globally attractiveness of periodic solution for predator-free and prey-free systems are presented. Secondly, by using comparison theorem of impulsive differential equation and other analysis methods, sufficient and necessary conditions on the permanence and extinction of prey species x with predator have other food source are established. Finally, the theoretical results both for non-autonomous system and corresponding autonomous system are confirmed by numerical simulations, from which we can see some interesting phenomena happen. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：4243 / 4256

页数：14

共 41 条

[21] EXISTENCE OF PERIODIC-SOLUTIONS OF NONLINEAR-SYSTEMS OF DIFFERENTIAL-EQUATIONS WITH IMPULSE EFFECT [J].

HRISTOVA, SG ;

BAINOV, DD .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1987, 125 (01) :192-202

[22] Dynamics of a stage-structured predator-prey model with prey impulsively diffusing between two patches [J].

Jiao, Jianjun ;

Chen, Lansun ;

Cai, Shaohong ;

Wang, Limin .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (04) :2748-2756

[23]

Lakshmikantham V., 1989, World scientific, V6

[24] DISPERSION AND POPULATION INTERACTIONS [J].

LEVIN, SA .

AMERICAN NATURALIST, 1974, 108 (960) :207-228

[25]

LEVINS R, 1969, Bulletin of the Entomological Society of America, V15, P237

[26] TWO PATCHES IMPULSIVE DIFFUSION PERIODIC SINGLE-SPECIES LOGISTIC MODEL [J].

Liu, Zijian ;

Teng, Zhidong ;

Zhang, Long .

INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2010, 3 (01) :127-141

[27] PERMANENCE AND GLOBAL STABILITY FOR COOPERATIVE LOTKA-VOLTERRA DIFFUSION-SYSTEMS [J].

LU, ZG ;

TAKEUCHI, Y .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1992, 19 (10) :963-975

[28]

SKELLAM JG, 1951, BIOMETRIKA, V38, P196, DOI 10.2307/2332328

[29] Dynamic behaviors of the periodic predator-prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect [J].

Song, Xinyu ;

Li, Yongfeng .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (01) :64-79

[30] PERMANENCE AND GLOBAL STABILITY FOR COMPETITIVE LOTKA-VOLTERRA DIFFUSION-SYSTEMS [J].

TAKEUCHI, Y ;

LU, ZY .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 24 (01) :91-104

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