Schedule Jul 30, 2001
Oscillations in Large Networks
Dr. Bard Ermentrout
http://www.pitt.edu/~phase/
The goal is to illustrate the phase reduction approach for rhythmic systems. In systems where the interactions between neurons is weak, in the sense that they can effect each others timing and not necessarily their rate of firing, it is possible to express the dynamics of the network solely in terms of pair-wise interactions between a phase variable for each neuron. The neurons themselves are represented as oscillators with a single dynamic variable, their phase. The dynamics of the phase variable can be semi-analytically deduced directly from the detailed biophysics of the cell. This approach, albeit useful only for weakly coupled rhythmically firing systems, shows how network properties may be deduced directly from the underlying biophysics of neurons and synapses.

The phase reduction has had a number of successes, which will be reviewed. These include the prediction of synchrony in networks of all inhibitory networks, the prediction of long-range connections in the spinal network of lamprey and leech, and the modeling of electrical waves in a variety of species.

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