The hunting cooperation of a predator under two prey's competition and fear-effect in the prey-predator fractional-order model

被引：23

作者：

Yousef, Ali ^{[1
]}

Thirthar, Ashraf Adnan ^{[2
]}

Alaoui, Abdesslem Larmani ^{[3
]}

Panja, Prabir ^{[4
]}

Abdeljawad, Thabet ^{[5
,6
]}

机构：

[1] Kuwait Coll Sci & Technol, Dept Math, Kuwait 2723, Kuwait

[2] Univ Fallujah, Dept Studies & Planning, Anbar, Iraq

[3] Moulay Ismail Univ, MAIS Lab, MAMCS Grp, FST Errachidia, Meknes, Morocco

[4] Haldia Inst Technol, Dept Appl Sci, Purba Midnapore 721657, W Bengal, India

[5] Prince Sultan Univ, Dept Math & Sci, POB 66833, Riyadh 11586, Saudi Arabia

[6] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 04期

关键词：

fear effect; Caputo fractional order; predator-prey model; stability; Neimark-Sacker bifurcation; STABILITY; DYNAMICS; SYSTEMS; FOOD;

D O I：

10.3934/math.2022303

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates a fractional-order mathematical model of predator-prey interaction in the ecology considering the fear of the prey, which is generated in addition by competition of two prey species, to the predator that is in cooperation with its species to hunt the preys. At first, we show that the system has non-negative solutions. The existence and uniqueness of the established fractional-order differential equation system were proven using the Lipschitz Criteria. In applying the theory of Routh-Hurwitz Criteria, we determine the stability of the equilibria based on specific conditions. The discretization of the fractional-order system provides us information to show that the system undergoes Neimark-Sacker Bifurcation. In the end, a series of numerical simulations are conducted to verify the theoretical part of the study and authenticate the effect of fear and fractional order on our model's behavior.

引用

页码：5463 / 5479

页数：17

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