On the Stability of Stationary States in Diffusion Models in Biology and Humanities

We consider an initial-boundary value problem for the system of partial differential equations describing processes of growth and spread of substance in biology, sociology, economics and linguistics. We note from a general point of view that adding diffusion (migration) terms to ordinary differentia...

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Detalles Bibliográficos
Autores principales: Polovinkina, M. V., Polovinkin, I. P.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Pleiades Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9522459/
http://dx.doi.org/10.1134/S1995080222090220
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author Polovinkina, M. V.
Polovinkin, I. P.
author_facet Polovinkina, M. V.
Polovinkin, I. P.
author_sort Polovinkina, M. V.
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description We consider an initial-boundary value problem for the system of partial differential equations describing processes of growth and spread of substance in biology, sociology, economics and linguistics. We note from a general point of view that adding diffusion (migration) terms to ordinary differential equations, for example, to logistic ones, can in some cases improve sufficient conditions for the stability of a stationary solution. We give examples of models in which the addition of diffusion terms to ordinary differential equations changes the stability conditions of a stationary solution.
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spelling pubmed-95224592022-09-30 On the Stability of Stationary States in Diffusion Models in Biology and Humanities Polovinkina, M. V. Polovinkin, I. P. Lobachevskii J Math Article We consider an initial-boundary value problem for the system of partial differential equations describing processes of growth and spread of substance in biology, sociology, economics and linguistics. We note from a general point of view that adding diffusion (migration) terms to ordinary differential equations, for example, to logistic ones, can in some cases improve sufficient conditions for the stability of a stationary solution. We give examples of models in which the addition of diffusion terms to ordinary differential equations changes the stability conditions of a stationary solution. Pleiades Publishing 2022-09-29 2022 /pmc/articles/PMC9522459/ http://dx.doi.org/10.1134/S1995080222090220 Text en © Pleiades Publishing, Ltd. 2022 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Polovinkina, M. V.
Polovinkin, I. P.
On the Stability of Stationary States in Diffusion Models in Biology and Humanities
title On the Stability of Stationary States in Diffusion Models in Biology and Humanities
title_full On the Stability of Stationary States in Diffusion Models in Biology and Humanities
title_fullStr On the Stability of Stationary States in Diffusion Models in Biology and Humanities
title_full_unstemmed On the Stability of Stationary States in Diffusion Models in Biology and Humanities
title_short On the Stability of Stationary States in Diffusion Models in Biology and Humanities
title_sort on the stability of stationary states in diffusion models in biology and humanities
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9522459/
http://dx.doi.org/10.1134/S1995080222090220
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