A delayed prey-predator model with Crowley-Martin-type functional response including prey refuge

被引：28

作者：

Maiti, Atasi Patra ^{[1
]}

Dubey, B. ^{[2
]}

Tushar, Jai ^{[2
]}

机构：

[1] IIT Kharagpur, Ctr Ocean River Atmosphere & Land Sci, Kharagpur 721302, W Bengal, India

[2] Birla Inst Technol & Sci, Pilani 333031, Rajasthan, India

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 16期

关键词：

Hopf bifurcation; delay; Crowley-Martin functional response; refuge; intra-specific interference; HOPF-BIFURCATION ANALYSIS; QUALITATIVE-ANALYSIS; MUTUAL INTERFERENCE; POSITIVE SOLUTIONS; DIFFUSION; STABILITY; FISHERY; SYSTEM; DYNAMICS; RESERVE;

D O I：

10.1002/mma.4429

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we have studied a prey-predator model living in a habitat that divided into two regions: an unreserved region and a reserved (refuge) region. The migration between these two regions is allowed. The interaction between unreserved prey and predator is Crowley-Martin-type functional response. The local and global stability of the system is discussed. Further, the system is extended to incorporate the effect of time delay. Then the dynamical behavior of the system is analyzed, taking delay as a bifurcation parameter. The direction of Hopf bifurcation and the stability of the bifurcated periodic solution are determined with the help of normal form theory and centre manifold theorem. We have also discussed the influence of prey refuge on densities of prey and predator species. The analytical results are supplemented with numerical simulations. Copyright (c) 2017 John Wiley & Sons, Ltd.

引用

页码：5792 / 5809

页数：18

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