Nonlinear Responses of Excitable Membranes

Abstract

Self-sustained oscillation of excitable membranes synchronizes with a periodic stimulation because of its nonlinearity. The oscillation, however, becomes irregular under some value of amplitude and frequency of the stimulation. The present review mainly shows the existence of the chaotic behavior of the Nitella internodal cell and the Onchidium silent neuron.
Stroboscopic representation of irregular oscillation forms a strange sttractor. Its hyperbolicity results from the nonlinear characteristics of the membrane, i. e., the threshold and the refractory period. The state points on the attractor are mixed by Baker, s transformation and the map is a convex function. The irregualr response is the chaos which is subject to the deterministic dynamics. The phase diagram of the nonlinear response was obtained in the Nitella cell; there exist the 1/n-harmonic (n is integer), the m/n-harmonic (m and n are integers, m≠1), the quasiperiodic and the chaotic oscillations.