A simple mathematical model of the chemically excitable membranes leading to autonomous chaotic oscillations is presented. The model assumes two kinds of autocatalytic ion channels, one is for cations and the other is for anions. Self-consistency between the ion distributions and the electric potentials is taken into account by including the counter ions explicitly. Cations and anions pass through their own channels with their permeabilities changing nonlinearly with the densities of ions at the surfaces of the membrane. Cation and anion transport systems then form two subsystems that oscillate and interact with each other through the membrane potential. When the coupling strength between the two ion systems and adsorption rate of ions to channels are varied, various types of chaotic oscillations are generated autonomously, i.e., without a stimulating periodic force. Experimental evidence to the present model is discussed. It is suggested that endogenous chaos in biological systems may appear from the electric coupling among different kinds of ion transport systems. © 1993.
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