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Research Article | Open Access

Traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey

Yujuan Jiao( ), Jinmiao Yang, Hang Zhang
College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, 730030, China
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Abstract

In this paper, we investigate the traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey. Firstly, using the upper and lower solutions method we prove the existence and non-existence of weak traveling wave solutions. Furthermore, we prove that the weak traveling wave solutions are actually traveling wave solutions under additional conditions by using Lyapunov function method and LaSalle's invariance principle.

Keywords

predator-prey modeltraveling wave solutionupper and lower solutionLyapunov functionLaSalle's invariance principle
CLC number: 34C37, 35C07

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16261-16277
DOI: 10.3934/math.2022888

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Cite this article:
Jiao Y, Yang J, Zhang H. Traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey. AIMS Mathematics, 2022, 7(9): 16261-16277. https://doi.org/10.3934/math.2022888

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Received: 20 April 2022
Revised: 14 June 2022
Accepted: 20 June 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)