Terman The investigator studies large networks of relaxation-type oscillators with coupling that mimics chemical synapses. These lead to large systems of differential equations that include numerous physical parameters as well as multiple time scales. The models typically display an incredibly rich structure of dynamic behavior; this depends in a highly nontrivial way on the various parameters. The investigator systematically studies what sorts of collective behavior are possible in a given network, determines the mathematical mechanisms responsible for this rich oscillatory behavior, classifies the sorts of bifurcations that can take place as parameters in the models are varied, and determines the physical consequences of the underlying mathematical structures. The types of networks considered in this project arise in numerous applications. These include several areas of the nervous system, respiration, movement, secretion, and models for scene segmentation. The project examines models for bursting oscillations in pancreatic beta cells. These cells are responsible for the secretion of insulin. It also analyzes models for oscillations in various parts of the nervous system, including the hippocampus and the thalamus. The investigator also continues a study of scene segmentation and other aspects of visual processing. This work contributes to fundamental understanding of pancreatic functions and a variety of neurophysiological questions.
