Hopf bifurcation analysis of a predator–prey model with Holling-II type functional response and a prey refuge

Yong Zhou; Wen Sun; Yinfang Song; Zhigang Zheng; Jinhu Lu; Shihua Chen

doi:10.1007/s11071-019-05063-w

Hopf bifurcation analysis of a predator–prey model with Holling-II type functional response and a prey refuge

Yong Zhou
, Wen Sun^*
, Yinfang Song
, Zhigang Zheng
, Jinhu Lu
, Shihua Chen

^*Corresponding author for this work

Yangtze University
Huaqiao University
CAS - Academy of Mathematics and System Sciences
Wuhan University

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

In this paper, a predator–prey model with Holling-II type functional response and a prey refuge is considered. The existence of Hopf bifurcations at the positive fixed point is established by analyzing its distribution of characteristic values. The stability and the directions of Hopf bifurcations of the model are derived for the variation of some crucial parameters. It is shown that these key parameters have a tremendous influence on the coexistence, the oscillation, and the stability of the considered model. Finally, numerical simulations are carried out to illustrate the validity of the results.

Original language	English
Pages (from-to)	1439-1450
Number of pages	12
Journal	Nonlinear Dynamics
Volume	97
Issue number	2
DOIs	https://doi.org/10.1007/s11071-019-05063-w
State	Published - 31 Jul 2019
Externally published	Yes

Keywords

Holling-II type
Hopf bifurcation
Refuge
The largest Lyapunov exponent

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10.1007/s11071-019-05063-w

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title = "Hopf bifurcation analysis of a predator–prey model with Holling-II type functional response and a prey refuge",

abstract = "In this paper, a predator–prey model with Holling-II type functional response and a prey refuge is considered. The existence of Hopf bifurcations at the positive fixed point is established by analyzing its distribution of characteristic values. The stability and the directions of Hopf bifurcations of the model are derived for the variation of some crucial parameters. It is shown that these key parameters have a tremendous influence on the coexistence, the oscillation, and the stability of the considered model. Finally, numerical simulations are carried out to illustrate the validity of the results.",

keywords = "Holling-II type, Hopf bifurcation, Refuge, The largest Lyapunov exponent",

author = "Yong Zhou and Wen Sun and Yinfang Song and Zhigang Zheng and Jinhu Lu and Shihua Chen",

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T1 - Hopf bifurcation analysis of a predator–prey model with Holling-II type functional response and a prey refuge

AU - Zhou, Yong

AU - Sun, Wen

AU - Song, Yinfang

AU - Zheng, Zhigang

AU - Lu, Jinhu

AU - Chen, Shihua

PY - 2019/7/31

Y1 - 2019/7/31

N2 - In this paper, a predator–prey model with Holling-II type functional response and a prey refuge is considered. The existence of Hopf bifurcations at the positive fixed point is established by analyzing its distribution of characteristic values. The stability and the directions of Hopf bifurcations of the model are derived for the variation of some crucial parameters. It is shown that these key parameters have a tremendous influence on the coexistence, the oscillation, and the stability of the considered model. Finally, numerical simulations are carried out to illustrate the validity of the results.

AB - In this paper, a predator–prey model with Holling-II type functional response and a prey refuge is considered. The existence of Hopf bifurcations at the positive fixed point is established by analyzing its distribution of characteristic values. The stability and the directions of Hopf bifurcations of the model are derived for the variation of some crucial parameters. It is shown that these key parameters have a tremendous influence on the coexistence, the oscillation, and the stability of the considered model. Finally, numerical simulations are carried out to illustrate the validity of the results.

KW - Holling-II type

KW - Hopf bifurcation

KW - Refuge

KW - The largest Lyapunov exponent

UR - https://www.scopus.com/pages/publications/85067691765

U2 - 10.1007/s11071-019-05063-w

DO - 10.1007/s11071-019-05063-w

M3 - 文章

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SN - 0924-090X

VL - 97

SP - 1439

EP - 1450

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

IS - 2

ER -

Hopf bifurcation analysis of a predator–prey model with Holling-II type functional response and a prey refuge

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Keywords

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