Summary: A simple model for synchronous firing of biological oscillators based on C. S. Peskin’s model of the cardiac pacemaker [Mathematical aspects of heart physiology (1975; Zbl 0301.92001), 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.