Boundedness and stabilization of a predator-prey model with attraction- repulsion taxis in all dimensions

Wenbin Lyu; Wenbin Lyu

doi:10.3934/mbe.2022629

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 13458-13482. doi: 10.3934/mbe.2022629

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Research article Special Issues

Boundedness and stabilization of a predator-prey model with attraction- repulsion taxis in all dimensions

Wenbin Lyu ^,

School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

Academic Editor: Zhi-An Wang

Received: 20 July 2022 Revised: 13 August 2022 Accepted: 22 August 2022 Published: 15 September 2022

This paper establishes the existence of globally bounded classical solutions to a predator-prey model with attraction-repulsion taxis in a smooth bounded domain of any dimensions with Neumann boundary conditions. Moreover, the global stabilization of solutions with convergence rates to constant steady states is obtained. Using the local time integrability of the $ L^2 $-norm of solutions, we build up the basic energy estimates and derive the global boundedness of solutions by the Moser iteration. The global stability of constant steady states is established based on the Lyapunov functional method.
- predator-prey,
- attraction-repulsion,
- global boundedness,
- global stability
Citation: Wenbin Lyu. Boundedness and stabilization of a predator-prey model with attraction- repulsion taxis in all dimensions[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 13458-13482. doi: 10.3934/mbe.2022629

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Abstract

This paper establishes the existence of globally bounded classical solutions to a predator-prey model with attraction-repulsion taxis in a smooth bounded domain of any dimensions with Neumann boundary conditions. Moreover, the global stabilization of solutions with convergence rates to constant steady states is obtained. Using the local time integrability of the $ L^2 $-norm of solutions, we build up the basic energy estimates and derive the global boundedness of solutions by the Moser iteration. The global stability of constant steady states is established based on the Lyapunov functional method.

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