Stochastic entrainment of a stochastic oscillator

Guanyu Wang, Charles Peskin

Research output: Contribution to journalArticle

Abstract

In this work, we consider a stochastic oscillator described by a discrete-state continuous-time Markov chain, in which the states are arranged in a circle, and there is a constant probability per unit time of jumping from one state to the next in a specified direction around the circle. At each of a sequence of equally spaced times, the oscillator has a specified probability of being reset to a particular state. The focus of this work is the entrainment of the oscillator by this periodic but stochastic stimulus. We consider a distinguished limit, in which (i) the number of states of the oscillator approaches infinity, as does the probability per unit time of jumping from one state to the next, so that the natural mean period of the oscillator remains constant, (ii) the resetting probability approaches zero, and (iii) the period of the resetting signal approaches a multiple, by a ratio of small integers, of the natural mean period of the oscillator. In this distinguished limit, we use analytic and numerical methods to study the extent to which entrainment occurs.

Original languageEnglish (US)
Article number052718
JournalPhysical Review E
Volume92
Issue number5
DOIs
StatePublished - Nov 25 2015

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Entrainment
entrainment
oscillators
Unit of time
Circle
Continuous-time Markov Chain
Markov chains
stimuli
infinity
integers
Numerical Methods
Infinity
Integer
Zero

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Stochastic entrainment of a stochastic oscillator. / Wang, Guanyu; Peskin, Charles.

In: Physical Review E, Vol. 92, No. 5, 052718, 25.11.2015.

Research output: Contribution to journalArticle

Wang, Guanyu ; Peskin, Charles. / Stochastic entrainment of a stochastic oscillator. In: Physical Review E. 2015 ; Vol. 92, No. 5.
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