Dynamical analysis of a fractional-order Rosenzweig-MacArthur model incorporating a prey refuge

被引：69
|
作者：
Moustafa, Mahmoud [1 ]
Mohd, Mohd Hafiz [1 ]
Ismail, Ahmad Izani [1 ]
Abdullah, Farah Aini [1 ]
机构：
[1] Univ Sains Malaysia, Sch Math Sci, Pulau 11800, Pinang, Malaysia
来源：
CHAOS SOLITONS & FRACTALS | 2018年 / 109卷
关键词：
Prey-predator model; Prey refuge; Fractional order system; Stability; Hopf bifurcation; Numerical simulation; PREDATOR-PREY; DIFFERENTIAL-EQUATIONS; STABILITY; DISCRETIZATION; SYSTEM; BIFURCATION; BEHAVIORS; FOOD;
D O I：
10.1016/j.chaos.2018.02.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper considers a fractional order Rosenzweig-MacArthur (R-M) model incorporating a prey refuge. The model is constructed and analyzed in detail. The existence, uniqueness, non-negativity and boundedness of the solutions as well as the local and global asymptotic stability of the equilibrium points are studied. Sufficient conditions for the stability and the occurrence of Hopf bifurcation for the fractional order R-M model are demonstrated. The resolution of the paradox of enrichment is investigated. The impact of fractional order and the prey refuge effects on the stability of the system are also studied both theoretically and by using numerical simulations. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1 / 13
页数：13
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