Dynamics of encoding in neuron populations: Some general mathematical features

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