Brette, R. (2007). Exact simulation of integrate-and-fire models with exponential currents. Neural Comput 19(10): 2604-2609.

Abstract. Neural networks can be simulated exactly using event-driven strategies, in which the algorithm advances directly from one spike to the next spike. It applies to neuron models for which we have 1) an explicit expression for the evolution of the state variables between spikes and 2) an explicit test on the state variables which predicts whether and when a spike will be emitted. In a previous work, we proposed a method which allows exact simulation of an integrate-and-fire model with exponential conductances, with the constraint of a single synaptic time constant. In this note we propose a method, based on polynomial root finding, which applies to integrate-and-fire models with exponential currents, with possibly many different synaptic time constants. Models can include biexponential synaptic currents and spike-triggered adaptation currents.

Download code:

• Scilab implementation of functions for exact simulation and an example script for a random network: ScilabExpIF.zip. The archive includes an event-driven simulator written in Scilab for networks with random external events and without delays (this is for pedagogical purposes and is not intended to be efficient at all). N.B.: Scilab is a free scientific software (resembling Matlab).
• C++ implementation of the same example: EventDrivenExpIF.zip (with the algorithm from the paper) and ClockDrivenExpIF.zip (with a standard clock-driven algorithm).