Synchronous Fireflies

At night in some parts of southeast Asia, thousands of male fireflies gather in the trees and flash on and off in unison. (A videotape of this spectacular phenomenon will be shown.) Such collective synchronization occurs throughout all of biology, from chorusing crickets to the rhythmic firing of cardiac pacemaker cells. In this talk, I will discuss a simple mathematical model for synchronization in a population of N coupled oscillators. The main theorem is that for all N and for almost all initial conditions, the model evolves to a state where all the oscillators are firing synchronously. Some good open problems for undergraduate investigation will be mentioned. (This is joint work with Rennie Mirollo, Boston College.)