A mathematical study of effects of narrow gap width in myelinated nerve axons (Q1175663)

Based on \textit{P. Grinrod's} [see Ordinary and partial differential equations, Proc. 8th Conf., Dundee/Scotl. 1984, Lect. Notes Math. 1151, 183-191 (1985; Zbl 0579.92003)] model of excitation propagation over a myelinated axon, the authors study the effects of the node gap width and the length of the myelinated part on the success and failure of propagation. The existence and nonexistence of two stationary solutions depending on a threshold value of the length of the myelinated part is proved. One of the stationary solutions is proved to be stable. Both stationary solutions are decreasing on the successive patches of the infinite axon. These results are interpreted by the authors physiologically as `` blocking of the propagation of the impulse if the unmyelinated gap is too large''. Numerical experiments are presented as well.