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Dynamics of Encoding in Neuron Populations: Some General Mathematical Features

Laboratory of Biophysics, Rockefeller University, and Laboratory of Applied Mathematics, Mount Sinai Medical School, New York University, New York, NY 10021, U.S.A.

The use of a population dynamics approach promises efficient simulation of large assemblages of neurons. Depending on the issues addressed and the degree of realism incorporated in the simulated neurons, a wide range of different population dynamics formulations can be appropriate. Here we present a common mathematical structure that these various formulations share and that implies dynamical behaviors that they have in common. This underlying structure serves as a guide toward efficient means of simulation. As an example, we derive the general population firing-rate frequency-response and show how it may be used effectively to address a broad range of interacting-population response and stability problems. A few specific cases will be worked out. A summary of this work appears at the end, before the appendix.

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