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Exact digital simulation of time-invariant linear systems with applications to neuronal modeling.
Rotter S, Diesmann M.
Neurobiologie und Biophysik, Institut fur Biologie III, Universitat Freiburg, Freiburg, Germany. rotter@biologie.uni-freiburg.de
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.
PMID: 10592015 [PubMed - indexed for MEDLINE]
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