title: Voltage-stepping schemes for the simulation of spiking neural networks.
abstract: 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.
authors.affiliation: INRIA, Inovallée 655 Avenue de l'Europe Montbonnot, 38334, Saint Ismier, France. Gang.Zheng@inrialpes.fr
authors.forename: G
authors.initials: G
authors.lastname: Zheng
authors.forename: A
authors.initials: A
authors.lastname: Tonnelier
authors.forename: D
authors.initials: D
authors.lastname: Martinez
mesh_terms: D000200:Action Potentials; D000465:Algorithms; D003198:Computer Simulation; D004553:Electric Conductivity; D008564:Membrane Potentials; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology; D013997:Time Factors