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Entrainment in the master equation

Authors :
Michael Margaliot
Lars Grüne
Thomas Kriecherbauer
Source :
Royal Society Open Science, Vol 5, Iss 4 (2018)
Publication Year :
2018
Publisher :
The Royal Society, 2018.

Abstract

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.

Details

Language :
English
ISSN :
20545703 and 68865686
Volume :
5
Issue :
4
Database :
Directory of Open Access Journals
Journal :
Royal Society Open Science
Publication Type :
Academic Journal
Accession number :
edsdoj.688656861ce6409fbe68e4ec04995f75
Document Type :
article
Full Text :
https://doi.org/10.1098/rsos.172157