Memristive Model of Excitable Cells

Abstract: This paper presents in-depth analysis of the excitable membranes of a biological system. We rigorously prove from the Chay neuron model that the state dependent voltage-sensitive potassium ion-channel and calcium sensitive potassium ion-channel in excitable cells are in-fact generic memristors and state independent mixed sodium and calcium ion-channel is non-memristive (nonlinear resistor) element in the perspective of electrical circuit theory. The mechanism to give the rise of the periodic oscillation, aperiodic (chaotic) oscillation, spikes and bursting in excitable cells are also analyzed via the small-signal model, pole-zero diagram, local-activity principle, edge of chaos and Hopf-bifurcation theorem. It is also shown that the presence of complex-conjugate and positive real part of zeros (equivalent to the Eigenvalues) of the admittance function inside the two bifurcation points lead to the generation of complicated electrical signals in excitable membrane.