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

An efficient new method for the exact digital simulation of time-invariant linear systems is presented. Such systems are frequently encountered as mod els for neuronal systems, or as submodules of such systems. The matrix expo nential is used to construct a matrix iteration, which propagates the dynam ic state of the system step by step on a regular time grid. A large and gen eral class of dynamic inputs to the system, including trains of delta-pulse s, can be incorporated into the exact simulation scheme. An extension of th e proposed scheme presents an attractive alternative for the approximate si mulation of networks of integrate-and-fire neurons with linear sub-threshol d integration and non-linear spike generation. The performance of the propo sed method is analyzed in comparison with a number of multi-purpose solvers . In simulations of integrate-and-fire neurons, Exact Integration systemati cally generates the smallest error with respect to both sub-threshold dynam ics and spike timing. For the simulation of systems where precise spike tim ing is important, this results in a practical advantage in particular at mo derate integration step sizes.