Nonlinear oscillations in chemical and biological systems

Abstract

The past decade has seen enormous progress in the study of nonlinear oscillations in chemical systems. In 1980, there were only two chemical oscillators, both accidentally discovered. Today, there are over two dozen, most designed using a systematic search procedure, and many understood at a mechanistic level. More complex phenomena such as spatial pattern formation, chaos and the behavior of coupled oscillators are the focus of current study. Certain aspects of biological systems, particularly in neurobiology, can be understood in terms of the behavior of coupled chemical oscillators. After giving a brief history of nonlinear chemical dynamics, we discuss the recent discovery and modeling of the stationary reaction-diffusion patterns predicted by Turing. We then look at a “very small neural network”, the crustacean stomatogastric ganglion. We conclude with some speculations on future directions in this area.