ctn-archive/technical-reports — pull request #2 by tbekolay (2014-12-08 16:42:58+00:00)
Title: WIP: Using Izhikevich neurons in Nengo

This is more an Issue than a PR; it's not even a WIP right now, more a reminder to myself to work on this at some point.

It's not clear right now what Izhikevich neurons are particularly good for in Nengo right now. This notebook should explore this.

Additionally, we use a few heuristics and tricks to make the neurons not blow up in Nengo, but we should do this in a more principled way. [Toubol, 2009](http://www.mitpressjournals.org/doi/abs/10.1162/neco.2009.09-08-853#.VIXT_ud4oWw) investigates this very issue, which is a good place to start in investigating this. If you really want to dig in, [Toubol & Brette, 2009](http://www-sop.inria.fr/members/Olivier.Faugeras/MVA/ArticlesALire09/SIADS-TouboulBrette09.pdf) seems like a great paper that discussed the Izhikevich neuron as just one of a class of QIF-like neurons with adaptation.

It may also be possible to get an analytical approximation of the instantaneous and asymptotic firing rates. There are lots of different cases for this, so it may be a lot of work to implement, but [Shlizerman & Holmes](http://faculty.washington.edu/shlizee/publications/rqif-det.pdf) appear to have worked out all the mathematical arguments required.