Geometric Analysis of Population Rhythms in Synaptically Coupled Neuronal Networks

We develop geometric dynamical systems methods to determine how various components contribute to a neuronal network's emergent population behavior. The results clarify the multiple roles inhibition can play in producing di erent rhythms. Which rhythms arise depends on how inhibition interacts with intrinsic properties of the neurons; the nature of these interactions depends on the underlying architecture of the network. Our analysis demonstrates that fast inhibitory coupling may lead to synchronized rhythms if either the cells within the network or the architecture of the network is su ciently complicated. This cannot occur in mutually coupled networks with simple cells; the geometric approach helps explain how additional network complexity allows for synchronized rhythms in the presence of fast inhibitory coupling. The networks and issues considered are motivated by recent models for thalamic oscillations. The analysis helps clarify the roles of various biophysical features, suc...

• Type: Journal
• Year: 2000
• Where: NECO
• Authors: Jonathan E. Rubin, David Terman
• Keywords: Geometric Dynamical Systems, Multiple Roles Inhibition, NECO 2000, Rhythms