Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis

We study the existence of global unique classical solution to a density-dependent prey-predator population system with indirect prey-taxis effect. With two Lyapunov functions appropriately constructed, we then show that the solution can asymptotically approach prey-only state or coexistence state of...

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Autor principal:	Yong Luo
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	density-dependent indirect prey-taxis lyapunov function asymptotical stability nonlinear semigroup Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/fa2e524b46704f13a3a6e9f870e34844
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spelling	oai:doaj.org-article:fa2e524b46704f13a3a6e9f870e348442021-11-12T01:36:36ZGlobal existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis10.3934/mbe.20213311551-0018https://doaj.org/article/fa2e524b46704f13a3a6e9f870e348442021-08-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021331?viewType=HTMLhttps://doaj.org/toc/1551-0018We study the existence of global unique classical solution to a density-dependent prey-predator population system with indirect prey-taxis effect. With two Lyapunov functions appropriately constructed, we then show that the solution can asymptotically approach prey-only state or coexistence state of the system under suitable conditions. Moreover, linearized analysis on the system at these two constant steady states shows their linear instability criterion. By numerical simulation we find that some density-dependent prey-taxis and predators' diffusion may either flatten the spatial one-dimensional patterns which exist in non-density-dependent case, or break the spatial two-dimensional distribution similarity which occurs in non-density-dependent case between predators and chemoattractants (released by prey).Yong LuoAIMS Pressarticledensity-dependentindirect prey-taxislyapunov functionasymptotical stabilitynonlinear semigroupBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 6672-6699 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	density-dependent indirect prey-taxis lyapunov function asymptotical stability nonlinear semigroup Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	density-dependent indirect prey-taxis lyapunov function asymptotical stability nonlinear semigroup Biotechnology TP248.13-248.65 Mathematics QA1-939 Yong Luo Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis
description	We study the existence of global unique classical solution to a density-dependent prey-predator population system with indirect prey-taxis effect. With two Lyapunov functions appropriately constructed, we then show that the solution can asymptotically approach prey-only state or coexistence state of the system under suitable conditions. Moreover, linearized analysis on the system at these two constant steady states shows their linear instability criterion. By numerical simulation we find that some density-dependent prey-taxis and predators' diffusion may either flatten the spatial one-dimensional patterns which exist in non-density-dependent case, or break the spatial two-dimensional distribution similarity which occurs in non-density-dependent case between predators and chemoattractants (released by prey).
format	article
author	Yong Luo
author_facet	Yong Luo
author_sort	Yong Luo
title	Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis
title_short	Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis
title_full	Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis
title_fullStr	Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis
title_full_unstemmed	Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis
title_sort	global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/fa2e524b46704f13a3a6e9f870e34844
work_keys_str_mv	AT yongluo globalexistenceandstabilityoftheclassicalsolutiontoadensitydependentpreypredatormodelwithindirectpreytaxis
_version_	1718431325933797376

Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis

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