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author:

Lai, Liyun (Lai, Liyun.) [1] | Yu, Xiangqin (Yu, Xiangqin.) [2] | He, Mengxin (He, Mengxin.) [3] | Li, Zhong (Li, Zhong.) [4] (Scholars:李忠)

Indexed by:

Scopus SCIE

Abstract:

We propose and study a Lotka-Volterra predator-prey system incorporating both Michaelis-Menten-type prey harvesting and fear effect. By qualitative analysis of the eigenvalues of the Jacobian matrix we study the stability of equilibrium states. By applying the differential inequality theory we obtain sufficient conditions that ensure the global attractivity of the trivial equilibrium. By applying Dulac criterion we obtain sufficient conditions that ensure the global asymptotic stability of the positive equilibrium. Our study indicates that the catchability coefficient plays a crucial role on the dynamic behavior of the system; for example, the catchability coefficient is the Hopf bifurcation parameter. Furthermore, for our model in which harvesting is of Michaelis-Menten type, the catchability coefficient is within a certain range; increasing the capture rate does not change the final number of prey population, but reduces the predator population. Meanwhile, the fear effect of the prey species has no influence on the dynamic behavior of the system, but it can affect the time when the number of prey species reaches stability. Numeric simulations support our findings.

Keyword:

Fear effect Lotka-Volterra predator-prey model Michaelis-Menten-type harvesting Stability

Community:

  • [ 1 ] [Lai, Liyun]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou, Peoples R China
  • [ 2 ] [Yu, Xiangqin]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou, Peoples R China
  • [ 3 ] [He, Mengxin]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou, Peoples R China
  • [ 4 ] [Li, Zhong]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou, Peoples R China

Reprint 's Address:

  • 李忠

    [Li, Zhong]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou, Peoples R China

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Source :

ADVANCES IN DIFFERENCE EQUATIONS

ISSN: 1687-1847

Year: 2020

Issue: 1

Volume: 2020

2 . 8 0 3

JCR@2020

3 . 1 0 0

JCR@2023

JCR Journal Grade:1

CAS Journal Grade:2

Cited Count:

WoS CC Cited Count: 7

SCOPUS Cited Count: 12

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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