具有恐惧效应的离散捕食者-食饵模型的稳定性

doi:10.13438/j.cnki.jdzk.2022.01.002

吉首大学学报（自然科学版） ›› 2022, Vol. 43 ›› Issue (1): 10-14.DOI: 10.13438/j.cnki.jdzk.2022.01.002

具有恐惧效应的离散捕食者-食饵模型的稳定性

舒晴，谢景力，刘晗嫣

(吉首大学数学与统计学院，湖南吉首 416000)

出版日期:2022-01-25 发布日期:2022-05-16
通讯作者: 谢景力（1972—）,男,湖南辰溪人,吉首大学数学与统计学院教授,博士,主要从事微分方程与动力系统及其应用研究.
基金资助:
湖南省教育厅科学研究项目(21C0373)

Stability of Discrete-Time Predator-Prey Model with Fear Effect

SHU Qing,XIE Jingli,LIU Hanyan

(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

Online:2022-01-25 Published:2022-05-16

摘要/Abstract

摘要：在经典的Leslie-Gower模型中引入常数能力收获和恐惧效应，通过动力系统的稳定性理论得到了捕食者-食饵模型在各平衡点的局部渐近稳定的条件，然后利用一个新判据获得了在正平衡点处发生Flip分岔的条件.数值模拟结果表明,适当地增加捕食者的收获可以稳定系统.

关键词： 恐惧效应, 常数能力收获, 捕食者-食饵模型, Leslie-Gower模型, 渐近稳定, Flip分岔

Abstract: The constant capacity harvesting and the fear effect are introduced into the classic Leslie-Gower model.Through the stability theory of the dynamical system,the local asymptotically stability conditions of the predator-prey model at each equilibrium point are obtained,and the condition of Flip bifurcation at the positive equilibrium is obtained by using a new critical criterion.Numerical simulations illustrate that an appropriate increase in harvesting of predators can stabilize the system.

Key words: fear effect, constant-effort harvesting, predator-prey model, Leslie-Gower model, asymptotically stable, Flip bifurcation

舒晴, 谢景力, 刘晗嫣. 具有恐惧效应的离散捕食者-食饵模型的稳定性[J]. 吉首大学学报（自然科学版）, 2022, 43(1): 10-14.

SHU Qing, XIE Jingli, LIU Hanyan. Stability of Discrete-Time Predator-Prey Model with Fear Effect[J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(1): 10-14.

参考文献

[1] WILSON EDWIN B.Elements of Physical Biology[J].Science，1927，66(1708)：281-282.
[2] VOLTERRA VITO.Fluctuations in the Abundance of a Species Considered Mathematically[J].Nature，1926，118(2972)：558-560.
[3] LESLIE P H，GOWER J C.The Properties of a Stochastic Model for the Predator-Prey Type of Interaction Between Two Species[J].Biometrika，1960，47(3/4)：219-234.
[4] HOLLING C S.The Functional Response of Predators to Prey Density and Its Role in Mimicry and Population Regulation[J].The Memoirs of the Entomological Society of Canada，1965，97(S45)：5-60.
[5] AZIZ-ALAOUI M A.Study of a Leslie-Gower-Type Tritrophic Population Model[J].Chaos，Solitons & Fractals，2002，14(8)：1275-1293.
[6] WANG Xiaoying，ZANETTE LIANA，ZOU Xingfu.Modelling the Fear Effect in Predator-Prey Interactions[J].Journal of Mathematical Biology，2016，73(5)：1179-1204.
[7] ZHANG Zizhen，UPADHYAY RANJIT KUMAR，DATTA JYOTISKA.Bifurcation Analysis of a Modified Leslie-Gower Model with Holling Type-IV Functional Response and Nonlinear Prey Harvesting[J].Advances in Difference Equations，2018，2018(1)：1-21.
[8] KHAN MUHAMMAD ASIF,SHABBIR MUHAMMAD SAJJAD,DIN QAMAR,et al.Chaotic Behavior of Harvesting Leslie-Gower Predator-Prey Model[J].Computational Ecology and Software,2019,9(3):67-88.
[9] XIE Jingli,LIU Hanyan,LUO Danfeng.The Effects of Harvesting on the Dynamics of a Leslie-Gower Model[EB/OL].(2021-05-06) [2021-08-22].https:∥www.hindawi.com/journals/ddns/2021/5520758/.
[10] FIRDIANSYAH ADIN LAZUARDY.Effect of Prey Refuge and Harvesting on Dynamics of Eco-Epidemiological Model with Holling Type III[J].Jambura Journal of Mathematics，2021，3(1)：16-25.
[11] MAY ROBERT M.Biological Populations with Nonoverlapping Generations：Stable Points，Stable Cycles，and Chaos[J].Science，1974，186(4164)：645-647.
[12] MAY ROBERT M.Simple Mathematical Models with Very Complicated Dynamics[J].Nature，1976，261：459-467.
[13] HASTINGS ALAN，POWELL THOMAS.Chaos in a Three-Species Food Chain[J].Ecology，1991，72(3)：896-903.
[14] KULENOVIC MUSTAFA R S，MERINO ORLANDO.Discrete Dynamical Systems and Difference Equations with Mathematica[M].New York：CRC Press，2002：97-102.
[15] WEN Guilin，CHEN Shijian，JIN Qiutan.A New Criterion of Period-Doubling Bifurcation in Maps and Its Application to an Inertial Impact Shaker[J].Journal of Sound and Vibration，2008，311(1/2)：212-223.

具有恐惧效应的离散捕食者-食饵模型的稳定性

Stability of Discrete-Time Predator-Prey Model with Fear Effect

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