Networks and Heterogeneous Media (NHM)

The derivation of continuum limits of neuronal networks with gap-junction couplings
Pages: 111 - 133, Issue 1, March 2014

doi:10.3934/nhm.2014.9.111      Abstract        References        Full text (2640.9K)           Related Articles

Claudio Canuto - Department of Mathematical Sciences, Corso Duca degli Abruzzi 29, 10129 Torino, Italy (email)
Anna Cattani - Department of Mathematical Sciences, Corso Duca degli Abruzzi 29, 10129 Torino, Italy (email)

1 R. B. Bapat, D. Kalita and S. Pati, On weighted directed graphs, Linear Algebra Appl., 436 (2012), 99-111.       
2 A. Cattani, "Multispecies'' Models to Describe Large Neuronal Networks, Ph.D. Thesis Polytechnic University of Turin, 2014.
3 P. Colli Franzone and G. SavarĂ©, Degenerate evolution systems modeling the cardiac electric field at micro- and macroscopic level, in Evolution Equations, Semigroups and Functional Analysis (Milano, 2000), Progress in Nonlinear Differential Equations and their Applications, 50, Birkhäuser, Basel, 2002, 49-78.       
4 G. B. Ermentrout and D. H Terman, Mathematical Foundations of Neuroscience, 1st edition, Springer, New York, 2010.       
5 R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophysical Journal, 1 (1961), 445-466.
6 R. FitzHugh, Motion picture of nerve impulse propagation using computer animation, J. Appl. Physiol., 25 (1968), 628-630.
7 M. Galarreta and S. Hestrin, Electrical synapses between Gaba-Releasing interneurons, Nature Reviews Neuroscience, 2 (2001), 425-433.
8 A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application in conduction and excitation in nerve, J. Physiol., 117 (1952), 500-544.
9 J. Keener and J. Sneyd, Mathematical Physiology, 1st edition, Springer-Verlag, New York, 1998.       
10 E. Marder, Electrical synapses: rectification demystified, Current Biology: CB, 19 (2009), R34-R35.
11 J. D. Murray, Mathematical Biology I, An Introduction, 3rd edition, Springer-Verlag, New York, 2002.       
12 S. Sanfelici, Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology, Numer. Methods Partial Differential Equations, 18 (2002), 218-240.       
13 A. C. Scott, The electrophysics of a nerve fiber, Review of Modern Physics, 47 (1975), 487-533.
14 J. Smoller, Shock Waves and Reaction-Diffusion Equations, 2nd edition, Springer-Verlag, New York, 1994.       
15 P. Wallisch, M. Lusignan, M. Benayoun, T. I. Baker, A. S. Dickey and N. G. Hatsopoulos, Matlab for Neuroscientists, Elsevier/Academic Press, Amsterdam, 2009.       
16 Y. C. Yu, S. He, S. Chen, Y. Fu, K. N. Brown, X.-H. Yao, J. Ma, K. P. Gao, G. E. Sosinsky, K. Huang and S. H. Shi, Preferential electrical coupling regulates neocortical lineage-dependent microcircuit assembly, Nature, 486 (2012), 113-117.

Go to top