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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...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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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. |
format | Online Article Text |
id | pubmed-7999843 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT birotamass transientdynamicsintherandomgrowthandresetmodel AT csillaglehel transientdynamicsintherandomgrowthandresetmodel AT nedazoltan transientdynamicsintherandomgrowthandresetmodel |