Boundedness and asymptotic behavior in a predator-prey model with indirect pursuit-evasion interaction

Chao Liu; Bin Liu

doi:10.3934/dcdsb.2021255

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2022, Volume 27, Issue 9: 4855-4874. Doi: 10.3934/dcdsb.2021255

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Boundedness and asymptotic behavior in a predator-prey model with indirect pursuit-evasion interaction

Chao Liu^1,2, and
Bin Liu^1,2, ,

1.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
2.
Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

^* Corresponding author: Bin Liu
^* Corresponding author: Bin Liu

Received: May 2021

Revised: August 2021

Early access: October 2021

Published: September 2022

This work is supported by National Natural Science Foundation of China grant 11971185

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Abstract

In this paper, we study the prey-predator model with indirect pursuit-evasion interaction defined on a smooth bounded domain with homogeneous Neumann boundary conditions. We obtain the globa existence and boundedness of the classical solution of the model by estimating $ L^{p} $-norm of $ u $ and $ v $, and we also show the large time behavior and convergence rate of the solution.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35A01, 35K57, 35Q92.

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Figure 1. Stabilization to the coexistence steady state

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Figure 2. Stabilization to the coexistence steady state

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Figure 3. Stabilization to the coexistence steady state

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Figure 4. Stabilization to the coexistence steady state

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