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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...

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Detalles Bibliográficos
Autores principales: Margaliot, Michael, Grüne, Lars, Kriecherbauer, Thomas
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2018
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.
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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
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