Physical approach of a second-order memristor in a neural circuit

In this article, a hybrid ion channel designed for second-order memristor in a neural circuit is explained from a physical aspect. Two kinds of memristors are combined with an inductor in one branch circuit of the neural circuit, and the channel current estimates the synchronous changes in physical field by introducing two different physical variables into the mem-conductance. Circuit equations, energy function are provided for the memristor-based neural circuit with clear physical explanations. Furthermore, dynamical analysis and stochastic resonance under noisy excitations are presented in this physical model. The results present theoretical support for some biophysical neuron models with hybrid ion channels, in which the inner field are controlled by all static ions, diffusive intracellular ion and ions flow across the membrane channels, and the model shows some advantages than some models in which ion channels for calcium, potassium, sodium and leak current are described by a single independent variable.