Modeling Excitable Cells with Memristors

This paper presents an in-depth analysis of an excitable membrane of a biological system by proposing a novel approach that the cells of excitable membrane can be modeled as the networks of memristors. We provide compelling evidence from the Chay neuron model that the state-independent mixed ion-channel behaves as a nonlinear resistor, while the state-dependent voltage-sensitive potassium ion-channel and calcium-sensitive potassium ion-channel function as generic memristors from the perspective of electrical circuit theory. The mechanism to give the rise to the periodic oscillation, aperiodic (chaotic) oscillation, spikes and bursting in an excitable cell are also analyzed via small-signal model, pole-zero diagram of admittance functions, local activity, edge of chaos and Hopf bifurcation theorem. It is also proved that the zeros of the admittance functions are equivalent to the eigenvalues of the Jacobian matrix and the presence of the positive real parts of the eigenvalues between the two bifurcations points lead to the generation of complicated electrical signals in an excitable membrane. The innovative concepts outlined in this paper pave the way for a deeper understanding of the dynamic behavior of excitable cells, offering potent tools for simulating and exploring the fundamental characteristics of biological neurons.