Rotter S, Diesmann M
Neurobiologie und Biophysik, Institut für Biologie III, Universität Freiburg, Freiburg, Germany.
Biol Cybern. 1999 Nov;81(5-6):381-402. doi: 10.1007/s004220050570.
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.
提出了一种用于时不变线性系统精确数字仿真的高效新方法。此类系统常作为神经元系统的模型，或作为此类系统的子模块出现。利用矩阵指数构造矩阵迭代，在规则时间网格上逐步传播系统的动态状态。该精确仿真方案可纳入一大类通用的系统动态输入，包括一系列δ脉冲。所提方案的扩展为具有线性亚阈值积分和非线性脉冲生成的积分发放神经元网络的近似仿真提供了一种有吸引力的替代方法。与多种通用求解器相比，分析了所提方法的性能。在积分发放神经元的仿真中，精确积分在亚阈值动态和脉冲定时方面系统地产生最小误差。对于精确脉冲定时很重要的系统仿真，这尤其在中等积分步长时带来实际优势。
