Math 577 -- Dynamical Models of Neuronal Computation
Spring 2010
Drawing by Santiago Ramón y Cajal, linked from David Hubel's Eye, Brain, and Vision.
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Instructor:
Kevin
Lin
Time: TR 08:00-09:15 am
Office: Math 619
Office hours:
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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
- W Gerstner and W Kistler,
Spiking
Neuron Models (Cambridge University Press)
- P Dayan and LF Abbott, Theoretical Neuroscience (MIT
Press)
[ Access through Cognet ] [ Supplementary material ]
Recommended reading
-
E D Adrian, The Physical Background of Perception
(Oxford University Press)
- 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).
- F Rieke, D Warland, R de Ruyter van Steveninck, and W
Bialek,
Spikes: Exploring the Neural Code (MIT
Press)
Additional general references
- E R Kandel, J Schwartz, T Jessell, Principles of
Neural Science (McGraw-Hill)
- J Keener and J Sneyd, Mathematical
Physiology (Springer)
- C Koch and I Segev,
editors, Methods
in Neuronal Modeling (MIT Press)
- G Shepherd, The Synaptic Organization of the
Brain (Oxford University Press)
References on nonlinear dynamics
- E M
Izhikevich, Dynamical
Systems in Neuroscience: the Geometry of Excitability
and Bursting (MIT Press)
- 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:
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.