Firing activity in an N-type locally active memristor-based Hodgkin-Huxley circuit

Hodgkin-Huxley (HH) circuit can reproduce abundant neuronal firing activities, but it is hard to physically implement the HH circuit. To solve this issue, an implementable HH circuit with two N-type locally active memristors (LAMs) to respectively characterize its Na+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textrm{Na}}<^>+$$\end{document} and K+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textrm{K}}<^>+$$\end{document} channels is proposed in this paper. Numerical explorations demonstrate that the N-type LAM-based Hodgkin-Huxley (N-LAM-HH) circuit can effectively generate periodic and chaotic firing activities. Moreover, a PCB-based hardware circuit is physically implemented and experimental measurement is performed. The experimentally captured time-domain waveforms of chaotic and periodic firing activities well confirm the numerical explorations. These verify the feasibility of the LAM in characterizing Na+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textrm{Na}}<^>+$$\end{document} and K+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textrm{K}}<^>+$$\end{document} channels and the availability of the N-LAM-HH circuit in generating firing activities, which can assist us in building the memristor-based neuromorphic hardware and exploring spike-based applications