Global dynamics of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and prey-taxis

Jialu Tian; Ping Liu; Jialu Tian; Ping Liu

doi:10.3934/era.2022048

Electronic Research Archive

2022, Volume 30, Issue 3: 929-942. doi: 10.3934/era.2022048

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Global dynamics of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and prey-taxis

Jialu Tian ,
Ping Liu ^,

Y.Y.Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, China

Received: 14 September 2021 Revised: 28 November 2021 Accepted: 29 November 2021 Published: 02 March 2022

In this paper, our purpose is to discuss the global dynamics of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and prey-taxis under homogeneous Neumann boundary conditions. First, we derive that the global classical solutions of the system are globally bounded by taking advantage of the Morse's iteration of the parabolic equation, which further arrives at the global existence of classical solutions with a uniform-in-time bound. In addition, we establish the global stability of the spatially homogeneous coexistence steady states under certain conditions on parameters by constructing Lyapunov functionals.
- Leslie-Gower predator-prey,
- Beddington-DeAngelis response,
- global stability,
- boundedness,
- prey-taxis
Citation: Jialu Tian, Ping Liu. Global dynamics of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and prey-taxis[J]. Electronic Research Archive, 2022, 30(3): 929-942. doi: 10.3934/era.2022048

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Abstract

In this paper, our purpose is to discuss the global dynamics of a modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and prey-taxis under homogeneous Neumann boundary conditions. First, we derive that the global classical solutions of the system are globally bounded by taking advantage of the Morse's iteration of the parabolic equation, which further arrives at the global existence of classical solutions with a uniform-in-time bound. In addition, we establish the global stability of the spatially homogeneous coexistence steady states under certain conditions on parameters by constructing Lyapunov functionals.

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