Losing Amplitude and Saving Phase

Many chemical and biological phenomena are modeled as systems of coupled limit cycle oscillators. These models are inherently complex in that they involve often large numbers of coupled ordinary and partial differential equations. To understand any of the behavior of these systems, simplifying assumptions are made. One such assumption is that the individual oscillators are nearly identical and weakly coupled. In this case only the phase of the individual oscillators matters and so the coupled system becomes a smaller system on a k-torus. This technique has been applied to discrete systems [1–3] as well as to reaction-diffusion equation [4,5]. Many interesting aspects of chemical and biological systems can be understood by studying the simple phase-models [6–8]. For example, see the paper by Kopell in this volume.