Oscillations and other patterns of neuronal activity arise throughout the central nervous system.  This activity has been observed in sensory processing, motor activities, and learning, and has been implicated in the generation of sleep rhythms, epilepsy, and Parkinson tremors.  Oscillatory behavior also arises in such areas as respiration, movement and secretion.  Basic questions involve how these rhythms are generated, how they are modulated and what the behavioral correlates of the neuronal activities are.

 

Mathematical models for the neuronal activity often display an incredibly rich structure of dynamic behavior.  A primary focus of our research is to develop mathematical and numerical techniques for analyzing this behavior.  Another focus is to characterize how the intrinsic and synaptic properties of the neurons within a network interact to shape the network's emergent population rhythm.  This will hopefully help experimentalists and theoreticians to better interpret data, create more sophisticated models and design new experiments.