Journal of Computational Neuroscience

, Volume 26, Issue 3, pp 409–423 | Cite as

Voltage-stepping schemes for the simulation of spiking neural networks

  • G. ZhengEmail author
  • A. Tonnelier
  • D. Martinez


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.


Voltage-stepping Event-driven Time-stepping Spiking neural networks 



Research supported by the INRIA cooperative research initiative RDNR.


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.INRIASaint IsmierFrance
  2. 2.LORIACampus ScientifiqueVandoeuvre-lès-NancyFrance

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