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On the Performance of Voltage Stepping for the Simulation of Adaptive, Nonlinear Integrate-and-Fire Neuronal Networks

Mohamed Ghaith Kaabi 1 Arnaud Tonnelier 2 Dominique Martinez 1
1 CORTEX - Neuromimetic intelligence
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
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.
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Mohamed Ghaith Kaabi, Arnaud Tonnelier, Dominique Martinez. On the Performance of Voltage Stepping for the Simulation of Adaptive, Nonlinear Integrate-and-Fire Neuronal Networks. Neural Computation, Massachusetts Institute of Technology Press (MIT Press), 2011, 23 (5), pp.1187-1204. ⟨10.1162/NECO_a_00112⟩. ⟨inria-00611646⟩

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