Title data
Margaliot, Michael ; Grüne, Lars ; Kriecherbauer, Thomas:
Entrainment in the Master Equation.
In: Royal Society Open Science.
Vol. 5
(25 April 2018)
Issue 172157
.
 33 S..
ISSN 20545703
DOI: https://doi.org/10.1098/rsos.172157
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Project financing: 
Andere Israel Science Foundation Grant 410/15 

Abstract in another language
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 24h 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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Entrainment in the Master Equation. (deposited 23 Oct 2017 12:12)
 Entrainment in the Master Equation. (deposited 27 Apr 2018 08:13) [Currently Displayed]