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Entrainment in the master equation
The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biolo...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society Publishing
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5936934/ https://www.ncbi.nlm.nih.gov/pubmed/29765669 http://dx.doi.org/10.1098/rsos.172157 |
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author | Margaliot, Michael Grüne, Lars Kriecherbauer, Thomas |
author_facet | Margaliot, Michael Grüne, Lars Kriecherbauer, Thomas |
author_sort | Margaliot, Michael |
collection | PubMed |
description | The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology. |
format | Online Article Text |
id | pubmed-5936934 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | The Royal Society Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-59369342018-05-15 Entrainment in the master equation Margaliot, Michael Grüne, Lars Kriecherbauer, Thomas R Soc Open Sci Physics The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology. The Royal Society Publishing 2018-04-25 /pmc/articles/PMC5936934/ /pubmed/29765669 http://dx.doi.org/10.1098/rsos.172157 Text en © 2018 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Physics Margaliot, Michael Grüne, Lars Kriecherbauer, Thomas Entrainment in the master equation |
title | Entrainment in the master equation |
title_full | Entrainment in the master equation |
title_fullStr | Entrainment in the master equation |
title_full_unstemmed | Entrainment in the master equation |
title_short | Entrainment in the master equation |
title_sort | entrainment in the master equation |
topic | Physics |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5936934/ https://www.ncbi.nlm.nih.gov/pubmed/29765669 http://dx.doi.org/10.1098/rsos.172157 |
work_keys_str_mv | AT margaliotmichael entrainmentinthemasterequation AT grunelars entrainmentinthemasterequation AT kriecherbauerthomas entrainmentinthemasterequation |