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Voltage-stepping schemes for the simulation of spiking neural networks

Gang Zheng 1, * Arnaud Tonnelier 1 Dominique Martinez 2 
* Corresponding author
1 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
2 CORTEX - Neuromimetic intelligence
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The numerical simulation of spiking neural networks requires particular attention. On the one hand, time-stepping methods are generic but theyhardly reproduce accurately the short-time scale uctuations of spiking neurons and need specific treatments to avoid the errors associated with the dis-continuities of ntegrate-and-fire models. On the other hand, event-driven methods are exact but restricted to a limited class of models. We present here a oltage-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-stepping scheme: long time-steps are used when the neuron is slowly varying whereas small time-steps are used in periods of intense activity. Our method accurately approximates the neuronal dynamics and we show analytically that such a scheme leads to an high-order algorithm. We illustrate the voltage-stepping method on nonlinear integrate-and-fire models. In this situation, our method consists of an approximation of the original model by a voltage-dependent integrate-and-fire. We compare our method with time-stepping schemes of Runge-Kutta type.
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Submitted on : Thursday, June 11, 2009 - 12:40:58 PM
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Gang Zheng, Arnaud Tonnelier, Dominique Martinez. Voltage-stepping schemes for the simulation of spiking neural networks. Journal of Computational Neuroscience, Springer Verlag, 2009, 26 (3), pp.409-423. ⟨10.1007/s10827-008-0119-1⟩. ⟨inria-00189386v4⟩



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