Prog. Theor. Phys. Vol. 53 No. 2 (1975) pp. 305-314

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Theory of Wave Propagation in Nervous System

— An Example of Dissipative Structure in an Open System —

Yoji Aizawa, Yukie Shimatani and Yonosuke Kobatake

Faculty of Pharmaceutical Sceinces, Hokkaido University, Sapporo

(Received July 13, 1974)

Abstract:

Propagation of an action potential in a nervous cell is studied theoretically on the basis of the notion that the excitation of nerve membrane is a transition bteween two non-equilibrium steady states. Basic phenomenological equations are derived for the excitation process taking consideration of the long-range dissipative interaction caused by the electric eddy current. Numerical calculations of these equations, show the occurrence of a solitary wave of an action potential under appropriate initial and boundary conditions, where both the nonlinear effect of the eddy current and the non-markoffian effect of accumulation of ions at the membrane surface are shown to play a role in the apprearance of a nervous soliton. Characteristics of the nervous soliton are studied numerically by the use of a simplified basic equation, and compared with the other types of solitary waves, e.g., the KdV soliton in a shallow water wave and the Toda soliton in a lattice vibration.

URL : http://ptp.ipap.jp/link?PTP/53/305/
DOI : 10.1143/PTP.53.305

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Citing Article(s) :

Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 1241-1242 :
Fluctuations in Excitable Membrane

Yōji Aizawa and Yonosuke Kobatake
Progress of Theoretical Physics Vol. 56 No. 3 (1976) pp. 703-716 :
Synergetic Approach to the Phenomena of Mode-Locking in Nonlinear Systems

Yōji Aizawa
Progress of Theoretical Physics Vol. 56 No. 3 (1976) pp. 724-740 :
Pattern Formation in Oscillatory Chemical Reactions

Yoshiki Kuramoto and Tomoji Yamada