Abstract

A simple model for synchronous firing of biological oscillators based on Peskin’s model of the cardiac pacemaker [Mathematical aspects of heart physiology, Courant Institute of Mathematical Sciences, New York University, New York, 1975, pp. 268–278] is studied. The model consists of a population of identical integrate-and-fire oscillators. The coupling between oscillators is pulsatile: when a given oscillator fires, it pulls the others up by a fixed amount, or brings them to the firing threshold, whichever is less.
The main result is that for almost all initial conditions, the population evolves to a state in which all the oscillators are firing synchronously. The relationship between the model and real communities of biological oscillators is discussed; examples include populations of synchronously flashing fireflies, crickets that chirp in unison, electrically synchronous pacemaker cells, and groups of women whose menstrual cycles become mutually synchronized.

MSC codes

  1. 92A09
  2. 34C15
  3. 58F40

Keywords

  1. synchronization
  2. biological oscillators
  3. pacemaker
  4. integrate-and-fire

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Published In

cover image SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
Pages: 1645 - 1662
ISSN (online): 1095-712X

History

Submitted: 3 August 1989
Accepted: 15 December 1989
Published online: 10 July 2006

MSC codes

  1. 92A09
  2. 34C15
  3. 58F40

Keywords

  1. synchronization
  2. biological oscillators
  3. pacemaker
  4. integrate-and-fire

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