Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting

Mengxin He; Zhong Li; Mengxin He; Zhong Li

doi:10.3934/era.2024299

Electronic Research Archive

2024, Volume 32, Issue 11: 6424-6442. doi: 10.3934/era.2024299

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Research article

Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting

Mengxin He ¹,
Zhong Li ^{2
,
,}

1.
School of Computer and Big Data, Minjiang University, Fuzhou, Fujian 350108, China
2.
School of Mathematics and Statistics, Fuzhou University, Fuzhou, Fujian 350108, China

Received: 26 August 2024 Revised: 31 October 2024 Accepted: 13 November 2024 Published: 25 November 2024

A Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting is proposed in this paper. We show that the system admits at most two boundary equilibria, both of which are unstable. The degenerate positive equilibrium of the system is a cusp of codimension 2, and the system undergoes cusp-type Bogdanov-Takens bifurcation of codimension 2. Moreover, we prove that the system has a weak focus of order at most 3, and the system can undergo a degenerate Hopf bifurcation of codimension 3. Our results reveal that the constant-yield harvesting can lead to richer dynamic behaviors.
- Leslie-Gower,
- harvesting,
- Hopf bifurcation,
- Bogdanov-Takens bifurcation,
- Smith growth
Citation: Mengxin He, Zhong Li. Dynamic behaviors of a Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting[J]. Electronic Research Archive, 2024, 32(11): 6424-6442. doi: 10.3934/era.2024299

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Abstract

A Leslie-Gower predator-prey model with Smith growth and constant-yield harvesting is proposed in this paper. We show that the system admits at most two boundary equilibria, both of which are unstable. The degenerate positive equilibrium of the system is a cusp of codimension 2, and the system undergoes cusp-type Bogdanov-Takens bifurcation of codimension 2. Moreover, we prove that the system has a weak focus of order at most 3, and the system can undergo a degenerate Hopf bifurcation of codimension 3. Our results reveal that the constant-yield harvesting can lead to richer dynamic behaviors.

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