Dynamic analysis method of single ion channel neuron circuit

By using a cellular membrane capacitor and a potassium ion memristor to characterize the charge storage and memory function of a neuron, this paper modified the classical circuit model and got the mesoscopic circuit model of the Hodgkin-Huxley single ion channel neuron. Based on the classical circuit theory and quantum theory of mesoscopic circuits, the response of membrane voltage of neurons under the sinusoidal excitation was derived. The calculation results show that with the increase in the frequency of the excitation source, the voltage peak-peak value of the membrane of the neuron and its steady-state hysteresis loop area first increase and then decrease. In the classical circuit model, the frequency at which the voltage peak-peak value and the hysteresis loop area reach the maximum depends on the amplitude of the external excitation source, while in the mesoscopic circuit model, it only depends on the circuit parameters of the neuron and is independent of the external excitation, which can better describe the characteristics of neurons. The mesoscopic circuit model of neurons is beneficial to reveal the dynamic mechanism of neural networks and promote the development of brain science theory systems.