Research Interests

I am a mathematician by training interested in the emergent properties of "self-organizing" systems. Some of my early work (with L. N. Howard) examined how oscillating chemical systems could, in conjunction with diffusion, produce complex spatio-temporal patterns. In this work, we showed that the ability to make such patterns is very robust and almost independent of the mechanisms that produce the chemical oscillation in the absence of diffusion. More recently, my work has focused on problems at the boundary between mathematics and neurophysiology, especially the study of "central pattern generators" or networks of neurons that govern rhythmic motor behavior. One aim of the mathematics was to develop methods to understand the behavior of large networks in contexts in which lack of information about the network circuits prevents the construction of detailed biophysical models. Another body of work concerns the development of methods for understanding how dynamic behavior of individual cells and their synaptic interactions affects network behavior and how this behavior is changed by neuromodulators. The mathematics used in these investigations involve (sometimes large) systems of nonlinear ordinary differential equations for which analytical tools are created and applied. Other continuing research interests include geometric methods for analysis of systems with several time scales.

Membership Type


Election Year


Primary Section

Section 28: Systems Neuroscience

Secondary Section

Section 32: Applied Mathematical Sciences