Voltage-stepping schemes for the simulation of spiking neural networks

The original publication is available at www.springerlink.comInternational audienceThe numerical simulation of spiking neural networks requires particular attention. On the one hand, time-stepping methods are generic but theyhardly reproduce accurately the short-time scale uctuations of spiking neurons and need specific treatments to avoid the errors associated with the dis-continuities of ntegrate-and-fire models. On the other hand, event-driven methods are exact but restricted to a limited class of models. We present here a oltage-stepping scheme that combines the advantages of these two approaches and consists of a discretization of the voltage state-space. The numerical simulation is reduced to a local event-driven method that induces an implicit activity-dependent time-stepping scheme: long time-steps are used when the neuron is slowly varying whereas small time-steps are used in periods of intense activity. Our method accurately approximates the neuronal dynamics and we show analytically that such a scheme leads to an high-order algorithm. We illustrate the voltage-stepping method on nonlinear integrate-and-fire models. In this situation, our method consists of an approximation of the original model by a voltage-dependent integrate-and-fire. We compare our method with time-stepping schemes of Runge-Kutta type