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Analytical and Numerical Treatment of Continuous Ageing in the Voter Model
The conventional voter model is modified so that an agent’s switching rate depends on the ‘age’ of the agent—that is, the time since the agent last switched opinion. In contrast to previous work, age is continuous in the present model. We show how the resulting individual-based system with non-Marko...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9600966/ https://www.ncbi.nlm.nih.gov/pubmed/37420351 http://dx.doi.org/10.3390/e24101331 |
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author | Baron, Joseph W. Peralta, Antonio F. Galla, Tobias Toral, Raúl |
author_facet | Baron, Joseph W. Peralta, Antonio F. Galla, Tobias Toral, Raúl |
author_sort | Baron, Joseph W. |
collection | PubMed |
description | The conventional voter model is modified so that an agent’s switching rate depends on the ‘age’ of the agent—that is, the time since the agent last switched opinion. In contrast to previous work, age is continuous in the present model. We show how the resulting individual-based system with non-Markovian dynamics and concentration-dependent rates can be handled both computationally and analytically. The thinning algorithm of Lewis and Shedler can be modified in order to provide an efficient simulation method. Analytically, we demonstrate how the asymptotic approach to an absorbing state (consensus) can be deduced. We discuss three special cases of the age-dependent switching rate: one in which the concentration of voters can be approximated by a fractional differential equation, another for which the approach to consensus is exponential in time, and a third case in which the system reaches a frozen state instead of consensus. Finally, we include the effects of a spontaneous change of opinion, i.e., we study a noisy voter model with continuous ageing. We demonstrate that this can give rise to a continuous transition between coexistence and consensus phases. We also show how the stationary probability distribution can be approximated, despite the fact that the system cannot be described by a conventional master equation. |
format | Online Article Text |
id | pubmed-9600966 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-96009662022-10-27 Analytical and Numerical Treatment of Continuous Ageing in the Voter Model Baron, Joseph W. Peralta, Antonio F. Galla, Tobias Toral, Raúl Entropy (Basel) Article The conventional voter model is modified so that an agent’s switching rate depends on the ‘age’ of the agent—that is, the time since the agent last switched opinion. In contrast to previous work, age is continuous in the present model. We show how the resulting individual-based system with non-Markovian dynamics and concentration-dependent rates can be handled both computationally and analytically. The thinning algorithm of Lewis and Shedler can be modified in order to provide an efficient simulation method. Analytically, we demonstrate how the asymptotic approach to an absorbing state (consensus) can be deduced. We discuss three special cases of the age-dependent switching rate: one in which the concentration of voters can be approximated by a fractional differential equation, another for which the approach to consensus is exponential in time, and a third case in which the system reaches a frozen state instead of consensus. Finally, we include the effects of a spontaneous change of opinion, i.e., we study a noisy voter model with continuous ageing. We demonstrate that this can give rise to a continuous transition between coexistence and consensus phases. We also show how the stationary probability distribution can be approximated, despite the fact that the system cannot be described by a conventional master equation. MDPI 2022-09-21 /pmc/articles/PMC9600966/ /pubmed/37420351 http://dx.doi.org/10.3390/e24101331 Text en © 2022 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 (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Baron, Joseph W. Peralta, Antonio F. Galla, Tobias Toral, Raúl Analytical and Numerical Treatment of Continuous Ageing in the Voter Model |
title | Analytical and Numerical Treatment of Continuous Ageing in the Voter Model |
title_full | Analytical and Numerical Treatment of Continuous Ageing in the Voter Model |
title_fullStr | Analytical and Numerical Treatment of Continuous Ageing in the Voter Model |
title_full_unstemmed | Analytical and Numerical Treatment of Continuous Ageing in the Voter Model |
title_short | Analytical and Numerical Treatment of Continuous Ageing in the Voter Model |
title_sort | analytical and numerical treatment of continuous ageing in the voter model |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9600966/ https://www.ncbi.nlm.nih.gov/pubmed/37420351 http://dx.doi.org/10.3390/e24101331 |
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