Mathematical Sciences: Mapping the Dynamics of Neural Network

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Peck In this multidisciplinary project, the investigator at Ithaca College and his colleagues Guckenheimer and others at Cornell University focus upon studies of the stomatogastric ganglion. This small neural network with approximately 30 neurons is a central pattern generator that coordinates movement of the gastric mill and pylorus of crustacea. The investigators construct compartmental models of individual neurons based upon experimental measurements and amalgamate these into models for subnetworks. These systems provide a testbed for the development of algorithms to explore the bifurcations of dynamical systems. Particular attention is given to those aspects of the systems that involve multiple time scales. The goal of the project is to improve understanding of dynamical processes in biological systems, with an emphasis upon neural systems. The investigators work in a multidisciplinary setting, combining experiment and mathematical modeling, giving due attention to both mathematics and neuroscience, and ensuring that the two interact at all times in the work. The larger goals are pursued in the context of specific systems, namely the study of a small neural circuit that controls rhythmic motions in the foregut of lobsters. This model system has been chosen for its modest size and accessibility for experimental manipulation. The project aims to understand how neural systems switch among motor patterns and how they regulate these patterns.