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Hyperbolic wave features of an exact solution to a model for nerve pulse transmission. (English) Zbl 0961.92008

Nerve pulse transmission through an excited fibre is investigated by means of an exact solution to a hyperbolic governing model which can also take into account cumulative nonlinear effects different from those due to the ion current mechanisms. It is shown that if the initial pulse is localized, the resulting signal propagates at finite velocity along the fibre perturbing the initial nonequilibrium state. The behaviour of signal velocity and the role played in the wave process by the characteristic speeds, provided by the hyperbolic governing model, are highlighted.

MSC:

92C20 Neural biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35L50 Initial-boundary value problems for first-order hyperbolic systems
92C05 Biophysics
35L99 Hyperbolic equations and hyperbolic systems
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