A geometric approach for studying the role of inhibitory synaptic coupling in either synchronizing or desynchronizing neural oscillations is presented. This issue has been considered in numerous papers; however, most of these studies have considered very idealized models such as integrate-and-fire model neurons or networks of relaxation oscillators. The geometric analysis allows us to study more realistic models for the underlying neurons and determine how changing biophysical parameters may affect the emergent network behavior. I will demonstrate that fast inhibitory coupling can lead to synchronized rhythms and then apply these techniques to analyze recent models for the spindle sleep rhythm.

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