A three species dynamical system involving prey-predation, competition and commensalism

被引:16
|
作者
Gakkhar, Sunita [1 ]
Gupta, Komal [1 ]
机构
[1] Indian Inst Technol, Dept Math, Roorkee 247667, Uttarakhand, India
关键词
Hotting-type II response; Commensalism; Refuge; Persistence; Hopf bifurcation; LESLIE-GOWER; STABILITY ANALYSIS; COMPLEX DYNAMICS; MODEL;
D O I
10.1016/j.amc.2015.09.036
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, a three species dynamical system is explored. The system consisting of two logistically growing competing species and the third species acts as a predator as well as host. It is predating over second species with Holling type II functional response, while first species is benefited from the third species. In addition, the prey species move into a refuge to avoid high predation. The essential mathematical features of the proposed model are studied in terms of boundedness, persistence, local stability and bifurcation. The existence of transcritical bifurcations have been established about two axial points. It has been observed that survival of all three species may be possible due to commensalism. Numerical simulations have been performed to show the Hopf bifurcation about interior equilibrium point. The existence of period-2 solution is observed. Further, the bifurcations of codimension-2 have also been investigated. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码:54 / 67
页数:14
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