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.
Audio for this talk requires sound hardware, and RealPlayer or RealAudio
by