Biology Reference
In-Depth Information
what details are important and what dynamic properties of the system may be of
functional significance. Without some appreciation of the underlying biology, it is
often difficult, if not impossible, to ask the most interesting questions and provide the
most meaningful answers.
Students interested in pursuing work in mathematical neuroscience may want to
start with reading [
3
], which gives a detailed description of how methods from non-
linear dynamics have been used to address problems in neuroscience. The online
supplement to this chapter also gives some additional information on other discrete
models of neuronal networks and how they relate to ours.
6.9
SUPPLEMENTARY MATERIALS
The online appendix, additional files, and computer code associated with this article
can be found, in the online version, at
http://dx.doi.org/10.1016/B978-0-12-415780-4.
00024-7
and from the volume's website
http://booksite.elsevier.com/9780124157804
References
[1] Just W, Ahn S, Terman D. Neuronal Networks: A Discrete Model - Online
Supplement (Appendix 6). In: Mathematical Concepts and Methods in Modern
Biology: Using Modern Discrete Models (Robeva R, Hodge T, Eds). Eslevier;
2013. http://booksite.elsevier.com/9780124157804
[2] Neuron, Wikipedia.
http://en.wikipedia.org/wiki/Neuron
.
[3] Ermentrout G, Terman D. Mathematical foundations of neuroscience. Springer;
2010.
[4] Hodgkin A, Huxley A. A quantitative description of membrane current and its
application to conduction and excitation in nerve. J Physiol 1952;117:500-544.
[5] Terman D, Ahn S, Wang X, Just W. Reducing neuronal networks to discrete
dynamics. Physica D 2008;237:324-338.
[6] Elashvili A, Jibladze M, Pataraia D. Combinatorics of necklaces and hermite
reciprocity. J Algebraic Comb 1999;10:173-188.
[7] Ahn S, Just W. Digraphs vs. dynamics in discrete models of neuronal networks.
DCDS-B 2012;17:1365-1381.
[8] Gallery of named graphs, Wikipedia.
[9] Just, W., Ahn, S., and Terman, D. (2007). Minimal attractors in digraph system
models of neuronal networks.MBI Technical Report 68,
http://mbi.osu.edu/p
ub-
lications/reports2007.html
.
[10] Wolfram S. A new kind of science. Wolfram Media; 2002.
[11] Wormatlas,
http://www.wormatlas.org/
.
[12] Stomatogastric ganglion,
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