Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equatio...

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Main Author:	Khaled S. Al Noufaey
Format:	article
Language:	EN
Published:	MDPI AG 2021
Subjects:	reaction–diffusion equations prey-predator system Hopf bifurcation semi-analytical models chaotic dynamics Mathematics QA1-939
Online Access:	https://doaj.org/article/5c1bce0bb0c44d30b6b7f1137627c2d1
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id	oai:doaj.org-article:5c1bce0bb0c44d30b6b7f1137627c2d1
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spelling	oai:doaj.org-article:5c1bce0bb0c44d30b6b7f1137627c2d12021-11-25T19:07:40ZStability Analysis of a Diffusive Three-Species Ecological System with Time Delays10.3390/sym131122172073-8994https://doaj.org/article/5c1bce0bb0c44d30b6b7f1137627c2d12021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2217https://doaj.org/toc/2073-8994In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.Khaled S. Al NoufaeyMDPI AGarticlereaction–diffusion equationsprey-predator systemHopf bifurcationsemi-analytical modelschaotic dynamicsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2217, p 2217 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	reaction–diffusion equations prey-predator system Hopf bifurcation semi-analytical models chaotic dynamics Mathematics QA1-939
spellingShingle	reaction–diffusion equations prey-predator system Hopf bifurcation semi-analytical models chaotic dynamics Mathematics QA1-939 Khaled S. Al Noufaey Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays
description	In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.
format	article
author	Khaled S. Al Noufaey
author_facet	Khaled S. Al Noufaey
author_sort	Khaled S. Al Noufaey
title	Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays
title_short	Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays
title_full	Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays
title_fullStr	Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays
title_full_unstemmed	Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays
title_sort	stability analysis of a diffusive three-species ecological system with time delays
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/5c1bce0bb0c44d30b6b7f1137627c2d1
work_keys_str_mv	AT khaledsalnoufaey stabilityanalysisofadiffusivethreespeciesecologicalsystemwithtimedelays
_version_	1718410279657668608

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

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