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

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 tr...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 9; pp. 16261 - 16277
Main Authors Jiao, Yujuan, Yang, Jinmiao, Zhang, Hang
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
lasalle's invariance principle
lyapunov function
predator-prey model
traveling wave solution
upper and lower solution
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022888