Saeid Seydnejad - Department of Electrical Eng, University of Kerman , Kerman , Iran

Linear Modeling of a spiking neuron has always been a difficult task due to the nonlinear mechanism involved in the generation of action potentials. In this article the spike generation mechanism of a neuron is mapped into the vector space theory. Using expansion into basic functions it is shown that the solution of an Integrate - and - Fire neuronal model can be converted into a linear matric equation. This linear epuation is also extended to a group of neurons greatly simplifying their analysis.

Neuronal model . Integrate - and - Fire Model , Spiking Neurons , Action Potentials, Neuronal pools