Global dynamics and pattern formation for predator-prey system with density-dependent motion

Tingfu Feng; Leyun Wu; Tingfu Feng; Leyun Wu

doi:10.3934/mbe.2023108

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 2296-2320. doi: 10.3934/mbe.2023108

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Global dynamics and pattern formation for predator-prey system with density-dependent motion

Tingfu Feng ¹,
Leyun Wu ^{2
,
,}

1.
Department of Mathematics, Kunming University, Kunming, Yunnan, China
2.
Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

Academic Editor: Zhi-An Wang

Received: 15 September 2022 Revised: 12 October 2022 Accepted: 20 October 2022 Published: 18 November 2022

In this paper, we concern with the predator-prey system with generalist predator and density-dependent prey-taxis in two-dimensional bounded domains. We derive the existence of classical solutions with uniform-in-time bound and global stability for steady states under suitable conditions through the Lyapunov functionals. In addition, by linear instability analysis and numerical simulations, we conclude that the prey density-dependent motility function can trigger the periodic pattern formation when it is monotone increasing.
- global existence,
- asymptotic stability,
- pattern formation
Citation: Tingfu Feng, Leyun Wu. Global dynamics and pattern formation for predator-prey system with density-dependent motion[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 2296-2320. doi: 10.3934/mbe.2023108

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Abstract

In this paper, we concern with the predator-prey system with generalist predator and density-dependent prey-taxis in two-dimensional bounded domains. We derive the existence of classical solutions with uniform-in-time bound and global stability for steady states under suitable conditions through the Lyapunov functionals. In addition, by linear instability analysis and numerical simulations, we conclude that the prey density-dependent motility function can trigger the periodic pattern formation when it is monotone increasing.

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