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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 between 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 appearance 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.

Theory of Wave Propagation in Nervous System: An Example of Dissipative Structure in an Open System