Math 577 -- Dynamical Models of Neuronal Computation

Spring 2010

Drawing by Santiago Ramón y Cajal, linked from David Hubel's Eye, Brain, and Vision.

Instructor: Kevin Lin

Time: TR 08:00-09:15 am
Place: Math East 246
Math 320 (starting Tue 2/3)

Office: Math 619
Phone: 626-6628

Office hours: M/T/Th 2-3pm
Tue 2-3pm
Wed 9-11am
Effective Feb 8

Course web page:

General information

This course surveys mathematical models of neurons and networks of neurons and introduces some of the mathematical tools used to analyze such models. See the
course syllabus for more information about the topics covered.

Journal Club

There is a Theoretical Neuroscience Journal Club that meets every other week in the math building. In terms of topics, this course and the Journal Club are complementary: this course will be more mathematical and at the same time cover more basic material.

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)


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:

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.

This page was last updated on September 01, 2013.