Study of propagation of electric impulses in nerve fibers of living organisms

Abstract

The propagation of solitary electric impulses in nerve fiber of living organisms is considered on the basis of the model of the generalized KdVB equation. It is shown that the nonlinear dependence of the membrane permeability on pulse amplitude leads to increasing of a steepness of the pulse front, the diffusion processes, which level the concentration on both sides of the membrane, make the front flatter, and dispersion causes the pulse to blur due to the difference in the propagation velocities of the harmonics composing the pulse. It is found that if these competing processes balance each other, then the pulse propagates through the fiber with the constant velocity without changing its shape looking like a soliton. The case when a single electric impulse can transform to a sequence of solitary pulses is noted, and that can be perceived by a living organism as another signal different from that at the input of system.