Delays and Oscillations in Networks of Spiking Neurons---a Two-Timescale Analysis
Dotan Di Castro, Ron Meir and Irad Yavneh
(2006) Technical Report. Technion, Israel.

Abstract

We study networks of excitatory and inhibitory integrate and fire neurons within a Fokker-Planck delay partial differential equation (PDE) formalism. Explicit conditions are established for the emergence of oscillatory solutions, and for the amplitude of the ensuing oscillations, for relatively large values of the delays. By employing a two-timescale analysis, the full PDE is replaced in this limit by a discrete time iterative map. This asymptotic result is shown numerically to hold, to a good approximation, over a wide range of parameter values, leading to an accurate characterization of the behavior in terms of the underlying physical parameters.

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