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author:

Zhang, Mengxin (Zhang, Mengxin.) [1] | Li, Zhong (Li, Zhong.) [2] (Scholars:李忠)

Indexed by:

SCIE

Abstract:

In this article, we analyze the bifurcation of a modified LeslieGower system with Holling type II functional response and fear effect. We discuss the existence and stability of equilibria. The system admits at most two positive equilibria, where one is always a saddle and the other is an anti-saddle, and a unique degenerate equilibrium which is a cusp of codimension three. In addition, with the change of parameters, the system undergoes saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and cusp type degenerate Bogdanov-Takens bifurcation of codimension three. We show that the system has two limit cycles (i.e., the inner one is unstable and the outer one is stable), and then undergoes the bistable phenomena. Finally, the existence of bifurcations are verified by numerical simulations.

Keyword:

Bogdanov-Takens bifurcation cusp Fear effect Hopf bifurcation modified Leslie-Gower

Community:

  • [ 1 ] [Zhang, Mengxin]Fuzhou Univ, Sch Math & Stat, Fuzhou 350108, Fujian, Peoples R China
  • [ 2 ] [Li, Zhong]Fuzhou Univ, Sch Math & Stat, Fuzhou 350108, Fujian, Peoples R China

Reprint 's Address:

  • 李忠

    [Li, Zhong]Fuzhou Univ, Sch Math & Stat, Fuzhou 350108, Fujian, Peoples R China

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Source :

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

ISSN: 1531-3492

Year: 2025

Issue: 10

Volume: 30

Page: 3730-3760

1 . 3 0 0

JCR@2023

CAS Journal Grade:4

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 2

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