Synchronization of Pulse-Coupled Biological Oscillators

TLDR

A simple model for synchronous firing of biological oscillators based on Peskin’s cardiac pacemaker model is studied. The model comprises identical integrate‑and‑fire oscillators coupled pulsatilely, where a firing oscillator pulls others up by a fixed amount or to threshold, whichever is smaller. For almost all initial conditions, the population converges to perfect synchrony, and the model is linked to real biological systems such as fireflies, crickets, pacemaker cells, and menstrual cycles. © 2006 Wiley Periodicals, Inc., Journal of Futures Markets 26:417–448.

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.