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Transient Dynamics in the Random Growth and Reset Model

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contribu...

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Detalles Bibliográficos
Autores principales: Biró, Tamás S., Csillag, Lehel, Néda, Zoltán
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7999843/
https://www.ncbi.nlm.nih.gov/pubmed/33807507
http://dx.doi.org/10.3390/e23030306
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author Biró, Tamás S.
Csillag, Lehel
Néda, Zoltán
author_facet Biró, Tamás S.
Csillag, Lehel
Néda, Zoltán
author_sort Biró, Tamás S.
collection PubMed
description A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.
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spelling pubmed-79998432021-03-28 Transient Dynamics in the Random Growth and Reset Model Biró, Tamás S. Csillag, Lehel Néda, Zoltán Entropy (Basel) Article A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics. MDPI 2021-03-05 /pmc/articles/PMC7999843/ /pubmed/33807507 http://dx.doi.org/10.3390/e23030306 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Biró, Tamás S.
Csillag, Lehel
Néda, Zoltán
Transient Dynamics in the Random Growth and Reset Model
title Transient Dynamics in the Random Growth and Reset Model
title_full Transient Dynamics in the Random Growth and Reset Model
title_fullStr Transient Dynamics in the Random Growth and Reset Model
title_full_unstemmed Transient Dynamics in the Random Growth and Reset Model
title_short Transient Dynamics in the Random Growth and Reset Model
title_sort transient dynamics in the random growth and reset model
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7999843/
https://www.ncbi.nlm.nih.gov/pubmed/33807507
http://dx.doi.org/10.3390/e23030306
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