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J Comput Neurosci. 2009 Jun;26(3):409-23. doi: 10.1007/s10827-008-0119-1. Epub 2008 Nov 26.

Voltage-stepping schemes for the simulation of spiking neural networks.

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INRIA, Inovallée 655 Avenue de l'Europe Montbonnot, 38334, Saint Ismier, France.


The numerical simulation of spiking neural networks requires particular attention. On the one hand, time-stepping methods are generic but they are prone to numerical errors and need specific treatments to deal with the discontinuities of integrate-and-fire models. On the other hand, event-driven methods are more precise but they are restricted to a limited class of neuron models. We present here a voltage-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 discretization (time-steps automatically increase when the neuron is slowly varying). We show analytically that such a scheme leads to a high-order algorithm so that it accurately approximates the neuronal dynamics. The voltage-stepping method is generic and can be used to simulate any kind of neuron models. We illustrate it on nonlinear integrate-and-fire models and show that it outperforms time-stepping schemes of Runge-Kutta type in terms of simulation time and accuracy.

[Indexed for MEDLINE]

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