In this paper we theoretically investigate the dynamics of a membrane model under external electric stimulation. The system shows various types of oscillatory responses in the membrane potential when a sinusoidal AC electric current is superimposed on the DC current applied across the membrane. The behavior goes from periodic oscillations, P1, to bursting type oscillations via quasiperiodicity, when the frequency of the AC current is varied. The time series displaying these behaviors are characterized using the methods of Dynamical System Theory, namely, return map, Lyapunov exponents, power spectrum and capacity dimension. The results are discussed in relation to biological membranes under similar conditions.
membrane oscillations; nonlinear phenomena; quasiperiodicity; bursting; sinusoidal stimulation
