Advertisement

Biological Cybernetics

, Volume 81, Issue 5–6, pp 381–402 | Cite as

Exact digital simulation of time-invariant linear systems with applications to neuronal modeling

  • Stefan Rotter
  • Markus Diesmann
Article

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 δ-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.

Keywords

Neuronal Modeling Integration Step Practical Advantage Spike Timing Simulation Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Stefan Rotter
    • 1
  • Markus Diesmann
    • 1
  1. 1.Neurobiologie und Biophysik, Institut für Biologie III, Universität Freiburg, Freiburg, GermanyDE

Personalised recommendations