Dynamics of a neuron with a hybrid memristive ion channel

Abstract

From the viewpoint of the physical, the membrane potential of the biological neuron can be effectively expressed by applying a capacitor. The ion channel in the neuron model can be selected the electrical element the relative to electromagnetic field to estimate and describe. In this paper, a hybrid memristive ion channel is built by connecting an inductor in series to a charge-controlled memristor (CCM), and a neural circuit with a hybrid memristive ion channel is designed by paralleling a capacitor and a nonlinear resistor to both sides of the hybrid memristive ion channel. Furthermore, the oscillator model of neural circuit and its energy function are derived by using the Kirchhoff's Current Law (KCL), Kirchhoff's Voltage Law (KVL) and Helmholtz's theorem. Furthermore, an adaptive regulation law is designed for investigating the self-regulation of neurons. The results illustrate that electrical activities of the neuron model with a hybrid memristive ion channel can be controlled by the external electric field distribution, and its firing modes are also adjusted by the energy ratio of the capacitor to the total energy in the neural circuit. This study is helpful to build artificial neurons with mixed ion channels.