Periodic solutions of a nonautonomous predator-prey system with stage structure and time delays

被引：22

作者：

Xu, Rui ^{[1
]}

Wang, Zhiqiang ^{[1
]}

机构：

[1] Inst Shijiazhuang Mech Engn, Dept Math, Shijiazhuang 050003, Hebei Province, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2006年 / 196卷 / 01期

关键词：

stage structure; time delay; permanence; periodic solution; global stability;

D O I：

10.1016/j.cam.2005.08.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nonautonomous Lotka-Volterra type predator-prey model with stage structure and time delays is investigated. It is assumed in the model that the individuals in each species may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not feed on prey and do not have the ability to reproduce. By some comparison arguments we first discuss the permanence of the model. By using the continuation theorem of coincidence degree theory, sufficient conditions are derived for the existence of positive periodic solutions to the model. By means of a suitable Lyapunov functional, sufficient conditions are obtained for the uniqueness and global stability of the positive periodic solutions to the model. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：70 / 86

页数：17

共 21 条

[1] ANALYSIS OF A MODEL REPRESENTING STAGE-STRUCTURED POPULATION-GROWTH WITH STATE-DEPENDENT TIME-DELAY [J].

AIELLO, WG ;

FREEDMAN, HI ;

WU, J .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1992, 52 (03) :855-869

[2] A TIME-DELAY MODEL OF SINGLE-SPECIES GROWTH WITH STAGE STRUCTURE [J].

AIELLO, WG ;

FREEDMAN, HI .

MATHEMATICAL BIOSCIENCES, 1990, 101 (02) :139-153

[3] SPACE-LIMITED RECRUITMENT IN OPEN SYSTEMS - THE IMPORTANCE OF TIME DELAYS [J].

BENCE, JR ;

NISBET, RM .

ECOLOGY, 1989, 70 (05) :1434-1441

[4] PERIODIC TIME-DEPENDENT PREDATOR-PREY SYSTEMS [J].

CUSHING, JM .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1977, 32 (01) :82-95

[5] PERSISTENCE AND GLOBAL ASYMPTOTIC STABILITY OF SINGLE SPECIES DISPERSAL MODELS WITH STAGE STRUCTURE [J].

FREEDMAN, HI ;

WU, JH .

QUARTERLY OF APPLIED MATHEMATICS, 1991, 49 (02) :351-371

[6]

Gaines RE, 1977, COINCIDENCE DEGREE N, DOI DOI 10.1007/BFB0089537

[7]

Gopalsamy K., 2013, Stability and Oscillations in Delay Differential Equations of Population Dynamics, V74

[8] A stage structured predator-prey model and its dependence on maturation delay and death rate [J].

Gourley, SA ;

Kuang, Y .

JOURNAL OF MATHEMATICAL BIOLOGY, 2004, 49 (02) :188-200

[9] ANALYSIS OF A DELAYED 2-STAGE POPULATION-MODEL WITH SPACE-LIMITED RECRUITMENT [J].

KUANG, Y ;

SO, JWH .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1995, 55 (06) :1675-1696

[10] Recent progress on stage-structured population dynamics [J].

Liu, SQ ;

Chen, LS ;

Agarwal, R .

MATHEMATICAL AND COMPUTER MODELLING, 2002, 36 (11-13) :1319-1360

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