Implementing Some Mathematical Models of Spiking Neurons

Abstract

In this project we take various spiking neuron models, which are used in simulation or implementation of different spiking neural network applications; such as brain simulation and engineering problems. Biologically plausible and computational efficiency are the most important factors that will be taken in consideration in order to choose one from the available spiking neuron models. we have HodgkinHuxley Model (HH) is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations it’s normally Biologically plausible then we take three simple models of neurons in rodent brains (RTM, WB and Erisir models). These are similar models to Hodgkin-Huxley Model (HH) but with different parameter values finally Izhikevich Model is biologically plausible. As well as it is computationally efficient, as Izhikevich Model represented by two differential equations .The chosen model should be the best to fit and meet the application specifications. we are discussed these spiking neuron models mathematically and how it could be used in simulating hippocampus. As well as, this project considers valuable comparisons between these models which they are provided according to the biological plausibility, computational efficiency, number of variables and complexity.