Week of January 23 - Feb 8 chapter 3 (active channels)

Chapt 3 of the book (page 55-) Morris-Lecar model
- Bifurcations to limit cycles
- Type I/Type II
Other channels
Simple models page 55 exercise 4,6,8,9,11,13 (Due wed Feb 15)
- Integrate and fire
- Theta model

Week of Feb 13th

Chapter five - synaptic channels (one day only, no exercises)
Analysis of Neural excitability and Figures - all about bursting in here!
We start Noise - chapter 6 A short version of the material
- Here is an XPP file for computing first passage times for a simple scalar neuron model. The figure shows some histograms for (red I=0,sigma=0.2;green I=0,sigma=0.4; white I=-.1,sigma=.2)
- Here is an XPP file for computing the FI curve for a simple scalar neuron model. The plot shows the FI curve as sigma goes from 0 to 0.5.
- Here is a very complex XPP file to solve the first passage BVP using AUTO. The plot shows the results of this for sigma=1 and 0.1 Note AUTO has a bit of a problem when I is negative and large.
- The FI curve with noise can be approximated by the following function. Let F(I) be the deterministic curve and define
  
  L(x,b) =x/(1-exp(-b*x))
  As b gets large, L(x,b) approaches the curve max(x,0). So, 1/b is like the amount of noise and FI(I) = F(L(I,b)) is a decent fit. We will use something like this later when we create firing rate models.
Noise related homework: page 153: 1,2 (computer exercise);4,6,8

Neural oscillators

Start reading the chapter on oscillators
HOMEWORK: oscillator chapter: 7,23,26,27. I'd assign many more, but you wouldnt do 'em anyway.

Coupled cells

Weak coupling of oscillators Notes and HW and an ODE file
Kuramoto theory Strogatz'review
Weak coupling near bifurcations Homework
- Hopf
- SNIC
Slow coupling and firing rate reductions

Slice models/wave propagation

Single spike assumptions
Firing rate models

Asynchronous states

Neural networks Neural net dynamics - Randy Beer

Spatial models

Bumps
Waves
Spatially periodic behavior