Abstract
A numerical study of the coupled nerve fibre problem is given which verifies and extends the perturbation theory of Luzader. Pulses on adjacent fibres can couple together with two possible stable pulse separations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Adey, W. R. and S. N. Bawin. 1977. “Brain Interactions with Weak Electric and Magnetic Fields.”Neurosci. Res. Prog. Bull. 15, 1–129.
Arvanitaki, A. 1942. “Effects Evoked in an Axon by the Activity of a Contiguous One.”J. Neurophysiol. 5, 89–108.
Cannon, J. R. and R. E. Ewing. 1977. “Galerkin Procedures for Systems of Parabolic Partial Differential Equations Related to the Transmission of Nerve Impulses.” InNonlinear Diffusion, Ed. W. E. Fitzgibbon III and H. F. Walker. New york: Pitman.
Casten, R. G., H. Cohen and P. A. Lagerstrom. 1975. “Perturbation Analysis of an Approximation to Hodgkin-Huxley Theory.”Q. Appl. Math. 32, 365–402.
FitzHugh, R. 1968. “Impulse Propagation in a Nerve Fibre.” 16 mm cine film; see also: R. FitzHugh,J. Appl. Physiol. 25, 628–630 (1968).
— 1969. “Mathematical models of excitation and propagation in nerves.” InBiological Engineering. Ed. H. P. Schwan. New York: McGraw-Hill.
Gordon, P. 1965. “Nonsymmetric Difference Equations.”J. Soc. Indust. Appl. Math. 13, 667–673.
Gourlay, A. R. and G. R. McGuire. 1970. “General Hopscotch Algorithm for the Numerical Solution of Partial Differential Equations.”J. Inst. Math. Applics 7, 216–227.
— 1970. “Some Recent Methods for the Numerical Solution of Time-dependent Partial Differential Equations.”Proc. R. Soc. A323, 219–235.
Katz, B. and O. H. Schmit. 1940. “Electric Interaction between Two Adjacent Nerve Fibres.”J. Physiol. 97, 471–488.
Khalifa, A. K. A. 1979. “Theory and application of the collocation method with splines for ordinary and partial differential equations.” PhD thesis, Heriot-Watt University.
Luzader, S. D. 1979. “Neurophysics of parallel nerve fibres.” PhD thesis, University of Wisconsin.
Markin, V. S. 1970. “Electrical Interactions of Parallel Non-Myelinated Nerve Fibres. 1. Change in Excitability of the Adjacent Fibre. 2. Collective Conduction of Impulses.”Biophysics 15, 133–155 and 713–721.
— 1973. “Electrical Interaction of Parallel Non-Myelinated Nerve Fibres. 3. Interaction in Bundles. 4. Role of Anatomical Inhomogeneities of Nerve Trunks.”Biophysics 18, 324–332 and 539–547.
Nagumo, J. S., S. Arimoto and S. Yoshizawa. 1962. “An active pulse transmission line stimulating nerve axon.”Proc. IRE 50, 2061–2070.
Richtmyer, R. D. and K. W. Morton. 1967.Difference Methods for Initial-Value Problems. New York: Wiley-Interscience.
Rinzel, J. and J. B. Keller. 1973. “Travelling Wave Solutions of a Nerve Conduction Equation.”Biophys. J. 13, 1313–1337.
— 1977. “Repetitive Nerve Impulse Propagation: Numerical and Methods.” InNonlinear Diffusion, Ed. W. E. Fitzgibbon III and H. F. Walker. New York: Pitman.
Scott, A. C. and S. D. Luzader. 1979. “Coupled Solitary Waves in Neurophysics.”Phys. Scripta 20, 495–501.
— 1962. “Analysis of Nonlinear Distributed Systems.”Trans IRE CT-9, 192–195.
Scott, A. C. 1977.Neurophysics. Wiley-Interscience.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Eilbeck, J.C., Luzader, S.D. & Scott, A.C. Pulse evolution on coupled nerve fibres. Bltn Mathcal Biology 43, 389–400 (1981). https://doi.org/10.1007/BF02459429
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02459429