title: On the performance of voltage stepping for the simulation of adaptive, nonlinear integrate-and-fire neuronal networks.
abstract: In traditional event-driven strategies, spike timings are analytically given or calculated with arbitrary precision (up to machine precision). Exact computation is possible only for simplified neuron models, mainly the leaky integrate-and-fire model. In a recent paper, Zheng, Tonnelier, and Martinez (2009) introduced an approximate event-driven strategy, named voltage stepping, that allows the generic simulation of nonlinear spiking neurons. Promising results were achieved in the simulation of single quadratic integrate-and-fire neurons. Here, we assess the performance of voltage stepping in network simulations by considering more complex neurons (quadratic integrate-and-fire neurons with adaptation) coupled with multiple synapses. To handle the discrete nature of synaptic interactions, we recast voltage stepping in a general framework, the discrete event system specification. The efficiency of the method is assessed through simulations and comparisons with a modified time-stepping scheme of the Runge-Kutta type. We demonstrated numerically that the original order of voltage stepping is preserved when simulating connected spiking neurons, independent of the network activity and connectivity.
authors.affiliation: Unité Mixte de Recherche 7503, LORIA, CNRS, 54506 Vandoeuvre-lès-Nancy, France. mohamedghaith.kaabi@loria.fr
authors.forename: Mohamed Ghaith
authors.initials: MG
authors.lastname: Kaabi
authors.forename: Arnaud
authors.initials: A
authors.lastname: Tonnelier
authors.forename: Dominique
authors.initials: D
authors.lastname: Martinez
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000222:Adaptation, Physiological / Q000502:physiology; D000818:Animals; D003198:Computer Simulation / Q000592:standards*; D006801:Humans; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D011897:Random Allocation; D013569:Synapses / Q000502:physiology*