Global stability and bifurcation of time delayed prey-predator system incorporating prey refuge

被引：45
|
作者：
Jana, Soovoojeet [2 ]
Chakraborty, Milon [3 ]
Chakraborty, Kunal [1 ]
Kar, T. K. [2 ]
机构：
[1] Indian Natl Ctr Ocean Informat Serv, Informat Serv & Ocean Sci Grp, Hyderabad 500090, Andhra Pradesh, India
[2] Bengal Engn & Sci Univ, Dept Math, Sibpur 711103, Howrah, India
[3] Golahat Jr High Sch, Burdwan 713513, W Bengal, India
来源：
MATHEMATICS AND COMPUTERS IN SIMULATION | 2012年 / 85卷
关键词：
Prey-predator; Refuge; Delay; Hopf bifurcation; Global stability; STAGE STRUCTURE; QUALITATIVE-ANALYSIS; HOPF-BIFURCATION; MODEL; DYNAMICS;
D O I：
10.1016/j.matcom.2012.10.003
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
This paper describes a prey-predator model with Holling type II functional response incorporating prey refuge. The equilibria of the proposed system are determined and the behavior of the system is investigated around equilibria. Density-dependent mortality rate for the predator is considered as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the co-existing equilibrium point. Discrete-type gestational delay of predators is also incorporated on the system. The dynamics of the delay induced prey-predator system is analyzed. Delay preserving stability and direction of the system is studied. Global stability of the delay preserving system is shown. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：57 / 77
页数：21
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