Stability analysis of the coexistence equilibrium of a balanced metapopulation model

Abstract We analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another thro...

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Autores principales:	Shodhan Rao, Nathan Muyinda, Bernard De Baets
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/924963c5ccf440e5ac52ef34ff219280
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spelling	oai:doaj.org-article:924963c5ccf440e5ac52ef34ff2192802021-12-02T16:14:55ZStability analysis of the coexistence equilibrium of a balanced metapopulation model10.1038/s41598-021-93438-82045-2322https://doaj.org/article/924963c5ccf440e5ac52ef34ff2192802021-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-93438-8https://doaj.org/toc/2045-2322Abstract We analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another through dispersal or migration. We assume that the inter-patch migrations are detailed balanced and that the patches are identical with intra-patch dynamics governed by a mean-field ODE system with a coexistence equilibrium. By making use of an appropriate Lyapunov function coupled with LaSalle’s invariance principle, we are able to show that the coexistence equilibrium point within each patch is locally asymptotically stable if the inter-patch dispersal network is heterogeneous, whereas it is neutrally stable in the case of a homogeneous network. These results provide a mathematical proof confirming the existing numerical simulations and broaden the range of networks for which they are valid.Shodhan RaoNathan MuyindaBernard De BaetsNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Shodhan Rao Nathan Muyinda Bernard De Baets Stability analysis of the coexistence equilibrium of a balanced metapopulation model
description	Abstract We analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another through dispersal or migration. We assume that the inter-patch migrations are detailed balanced and that the patches are identical with intra-patch dynamics governed by a mean-field ODE system with a coexistence equilibrium. By making use of an appropriate Lyapunov function coupled with LaSalle’s invariance principle, we are able to show that the coexistence equilibrium point within each patch is locally asymptotically stable if the inter-patch dispersal network is heterogeneous, whereas it is neutrally stable in the case of a homogeneous network. These results provide a mathematical proof confirming the existing numerical simulations and broaden the range of networks for which they are valid.
format	article
author	Shodhan Rao Nathan Muyinda Bernard De Baets
author_facet	Shodhan Rao Nathan Muyinda Bernard De Baets
author_sort	Shodhan Rao
title	Stability analysis of the coexistence equilibrium of a balanced metapopulation model
title_short	Stability analysis of the coexistence equilibrium of a balanced metapopulation model
title_full	Stability analysis of the coexistence equilibrium of a balanced metapopulation model
title_fullStr	Stability analysis of the coexistence equilibrium of a balanced metapopulation model
title_full_unstemmed	Stability analysis of the coexistence equilibrium of a balanced metapopulation model
title_sort	stability analysis of the coexistence equilibrium of a balanced metapopulation model
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/924963c5ccf440e5ac52ef34ff219280
work_keys_str_mv	AT shodhanrao stabilityanalysisofthecoexistenceequilibriumofabalancedmetapopulationmodel AT nathanmuyinda stabilityanalysisofthecoexistenceequilibriumofabalancedmetapopulationmodel AT bernarddebaets stabilityanalysisofthecoexistenceequilibriumofabalancedmetapopulationmodel
_version_	1718384305251549184

Stability analysis of the coexistence equilibrium of a balanced metapopulation model

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