title: Exact digital simulation of time-invariant linear systems with applications to neuronal modeling.
abstract: An efficient new method for the exact digital simulation of time-invariant linear systems is presented. Such systems are frequently encountered as models for neuronal systems, or as submodules of such systems. The matrix exponential is used to construct a matrix iteration, which propagates the dynamic state of the system step by step on a regular time grid. A large and general class of dynamic inputs to the system, including trains of delta-pulses, can be incorporated into the exact simulation scheme. An extension of the proposed scheme presents an attractive alternative for the approximate simulation of networks of integrate-and-fire neurons with linear sub-threshold integration and non-linear spike generation. The performance of the proposed method is analyzed in comparison with a number of multi-purpose solvers. In simulations of integrate-and-fire neurons, Exact Integration systematically generates the smallest error with respect to both sub-threshold dynamics and spike timing. For the simulation of systems where precise spike timing is important, this results in a practical advantage in particular at moderate integration step sizes.
authors.affiliation: Neurobiologie und Biophysik, Institut für Biologie III, Universität Freiburg, Freiburg, Germany. rotter@biologie.uni-freiburg.de
authors.forename: S
authors.initials: S
authors.lastname: Rotter
authors.forename: M
authors.initials: M
authors.lastname: Diesmann
mesh_terms: D000818:Animals; D003198:Computer Simulation; D003491:Cybernetics; D005071:Evoked Potentials; D006801:Humans; D016014:Linear Models; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D013997:Time Factors