(This article was originally published at mages' blog, and syndicated at StatsBlogs.)

I discussed earlier how the action potential of a

neuron can be modelled via the Hodgkin-Huxely equations. Here I will present a simple model that describes how action potentials can be generated and propagated across neurons. The tricky bit here is that I use delay differential equations (DDE) to take into account the propagation time of the signal across the network.

My model is based on the paper:

*Epileptiform activity in a neocortical network: a mathematical model* by F. Giannakopoulos, U. Bihler, C. Hauptmann and H. J. Luhmann. The article presents a flexible and efficient modelling framework for:

- large populations with arbitrary geometry
- different synaptic connections with individual dynamic characteristics
- cell specific axonal dynamics

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**Tags:** bursting, dede, delay differential equations, deSolve, dynamical systems, FitzHugh-Nagumo, Hodgkin-Huxley, Hopf-Bifurcation, neuron, R, Tutorials