Abstract
This chapter discusses the problems of dynamics of a population of neurons with an electric interaction between them. We encounter electrical synapses in the nervous system relatively less than we do chemical synapses. The electrical transmission of signals between excitable cells was demonstrated for the first time by Furshpan and Potter in 1959 in experiments on the giant axons of crayfish. Soon electrical excitation transfer was found in the central nervous system, in heart muscle, and in receptor cells.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chua, L., & Yang, L. (1988a). Cellular neural networks: Theory. IEEE Transactions on Circuits and Systems, 35(10), 1257–1272.
Chua, L. O., & Yang, L. (1988b). Cellular neural networks: Applications. IEEE Transactions on Circuits and Systems, 35, 1273.
Eckert, R., Randall D., & Augustine, G. (1991). Animal physiology (Vol. 1). Moscow: Mir.
Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, 79(8), 2554–2558.
Hopfield, J. J. (1984). Neurons with gradual response have collective computational properties like those of two-state Neurons. Proceedings of the National Academy of Sciences, 81, 3088–3092.
Kashchenko, S. A., & Mayorov, V. V. (1995). Wave structures in cellular network from formal neurons of Hutchinson. Radio Engineering and Electronics, 40(6), 925–936.
Kashchenko, S. A., Mayorov, V. V., & Myachin, M. L. (1995). Oscillations in systems of equations with delay and differential diffusion, modelling local neural networks. Reports of the Russian Academy of Sciences, 344(3), 137–140.
Lebedev, A. N. (1990). Human memory, its mechanisms and limits. Research of memory (pp. 104–118). Moscow: Nauka.
Ochs, S. (1969). Fundamentals of neurology. Moscow: Mir.
Pappas, G., & Waxman, S. (1973). Ultrastructure of synapses. Physiology and pharmacology of synaptic transmission (pp. 7–30). Leningrad: Nauka.
Schade, J., & Ford, D. (1976). Fundamentals of neurology. Moscow: Mir.
Tasaki, I. (1971). Nervous excitement. Moscow: Mir.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Kashchenko, S. (2015). Model of the Neural System with Diffusive Interaction of Elements. In: Models of Wave Memory. Lecture Notes in Morphogenesis. Springer, Cham. https://doi.org/10.1007/978-3-319-19866-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-19866-8_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19865-1
Online ISBN: 978-3-319-19866-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)