Group 2 2012

Introduction

We are interested in studying the entrainment of pulse-coupled biological oscillators, specifically populations of fireflies. Many species of fireflies use bio-luminescent flashing to attract mates. When a group of fireflies flash together, each starting at arbitrary phases, natural observation indicates that over some finite time scale, they are likely to achieve entrainment, and synchronous oscillatory behavior will emerge. The mathematical foundation of such a system is developed thoroughly by Strogatz in (insert paper here). However, such a model does not account for the existence of natural barriers that may divide a system of fireflies into different populations that do not exhibit universal coupling. Therefore, with this premise in mind, we obtain our central question: "At what point of communication parameter variation will the fireflies be prevented from consistently achieving synchrony?"

(Photo here)

Background

Consider the scenario of a population of oscillators, each with identical parameters in amplitude and frequency, only distinguished by the their offset phases. Now, introduce another constraint, establishing that each oscillator is coupled equally to all others, regardless of their relative proximity. Under such conditions, the

Experimental Details

Put variables, hypotheses, and miscellaneous science here!

== Bibliography ==\ Strogatz, S. H., Exploring Complex Networks

Kuramoto, Y. Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).

Winfree, A. T. The Geometry of Biological Time (Springer, New York, 1980).

Collins, J. J. & Stewart, I. Coupled nonlinear oscillators and the symmetries of animal gaits. J. Nonlin. Sci. 3, 349–392 (1993).