Perturbed and Coupled Oscillators and Black Holes

Abstract

With the plethora of known biological oscillators, and their generally accepted importance, it is natural to ask what effects external perturbations can have on the subsequent oscillations. In his pioneering work on circadian rhythms in the 1960’s, A.T. Winfree asked this basic and deceptively simple question in a biological context in connection with his experimental work on the periodic emergence of the fruit fly, Drosophila melanogaster, from their pupae. Since then a series of spectacular discoveries of hitherto unknown properties of perturbed oscillators, spatially coupled oscillators, oscillators coupled to diffusion processes and so on (see, for example, Chapter 12 and Chapter 1, Volume II), have been made as a result of this simple yet profound question. Winfree has developed a new conceptual geometric theory of biological time, which poses many challenging and interesting mathematical problems. Winfree’s (2000) seminal book, which has a full bibliography, discusses the area in detail. He also gives numerous important examples of biological situations where a knowledge of such effects is crucial to understanding certain phenomena which are observed.