Delays and Oscillations in Networks of Spiking Neurons - a Two Time Scale Analysis Dotan Di Castro 1 , Ron Meir 1 , Irad Yavneh 2 Department of Electrical Engineering 1 and Computer Science 2 Technion, Israel August 10, 2008 Neural Computation, In Press Abstract Oscillations are a ubiquitous feature of many neural systems, spanning many or- ders of magnitude in frequency. One of the most prominent oscillatory patterns, with possible functional implications, is that occurring in the mammalian thalamo-cortical system during sleep. This system is characterized by relatively long delays (reaching up to 40 msec), and gives rise to low frequency oscillatory waves. Motivated by these phenomena, we study networks of excitatory and inhibitory integrate and fire neurons within a Fokker-Planck delay partial differential equation formalism, and establish ex- plicit conditions for the emergence of oscillatory solutions, and for the amplitude and period of the ensuing oscillations, for relatively large values of the delays. By employing a two time scale analysis, the full partial differential equation is replaced in this limit by a discrete time iterative map, leading to a relatively simple dynamic interpretation. 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. Our results provide a simple mechanis- tic explanation for one type of slow oscillation based on delayed inhibition, which may play an important role in the slow spindle oscillations occurring during sleep. More- over, they are consistent with experimental findings related to human motor behavior with visual feedback.