8901913 Kopell This project is to study a variety of questions relating to central pattern generators (C.P.G.'s), which are neural networks that govern the stereotypic aspects of rhymthmic motor activity. These networks often involve oscillating subnetworks or cells interacting with other oscillators or non-oscillating neurons. One of the most studied C.P.G.'s is a network that is roughly configured as a chain of oscillators. One goal of the mathematics is to intuit and test conjectures about general kinds of constraints on the connectivity, in order that the network be able to function appropriately. The current effort builds on former results and focuses on three areas: (1) the role of long-range coupling in the network, (2) the construction of networks not composed of modular oscillatory subpieces, but behaving like chains of discrete oscillators, (3) the interaction of the neural activity of the C.P.G. with the mechanical activity that it directs. In addition, work is proposed on issues arising from small invertebrate network C.P.G.'s. The focus of that work is to relate properties of the cells to emergent properties of the network. All work is to be done in coordination with experimentalists. Finally, some purely mathematical topics are proposed.
