Math 577 -- Dynamical Models of Neuronal Computation

Primary references

1. W Gerstner and W Kistler, Spiking Neuron Models (Cambridge University Press)

2. P Dayan and LF Abbott, Theoretical Neuroscience (MIT Press)
   [ Access through Cognet ] [ Supplementary material ]

Recommended reading

1. E D Adrian, The Physical Background of Perception (Oxford University Press)

2. D Hubel, Eye, Brain, and Vision (Scientific American Library)

   This is a very readable, nontechnical introduction to visual information processing. I think it's well worth owning a copy (if you can find one).

3. F Rieke, D Warland, R de Ruyter van Steveninck, and W Bialek, Spikes: Exploring the Neural Code (MIT Press)

Additional general references

1. E R Kandel, J Schwartz, T Jessell, Principles of Neural Science (McGraw-Hill)

2. J Keener and J Sneyd, Mathematical Physiology (Springer)

3. C Koch and I Segev, editors, Methods in Neuronal Modeling (MIT Press)

4. G Shepherd, The Synaptic Organization of the Brain (Oxford University Press)

References on nonlinear dynamics

1. E M Izhikevich, Dynamical Systems in Neuroscience: the Geometry of Excitability and Bursting (MIT Press)

2. S H Strogatz, Nonlinear Dynamics and Chaos (Perseus)

Software

You can download SoftCell, which was developed for 6.021J at MIT. You may need to download and install MATLAB to run this program. The University has a site license which lets you use this software for free.

Here are hhfield.m, hhsolve.m, and hhplot.m.

For basic phase plane analysis, try these programs by John Polking:

• pplane7.m
• dfield7.m

These are two separate programs. To run pplane7, download the file "pplane7.m" and start MATLAB in the same directory, then type pplane7 at the prompt. You should get a window showing the simulation. Similar instructions apply to dfield7.

You can also run Java versions of these programs directly in your browser. You will need to make sure that Java is enabled.

For more detailed analysis of dynamical systems, try XPPAUT.