Abstract
The dynamics of neurons consist of oscillating patterns of a membrane potential that underpin the operation of biological intelligence. The FitzHugh–Nagumo (FHN) model for neuron excitability generates rich dynamical regimes with a simpler mathematical structure than the Hodgkin–Huxley model. Because neurons can be understood in terms of electrical and electrochemical methods, here we apply the analysis of the impedance response to obtain the characteristic spectra and their evolution as a function of applied voltage. We convert the two nonlinear differential equations of FHN into an equivalent circuit model, classify the different impedance spectra, and calculate the corresponding trajectories in the phase plane of the variables. In analogy to the field of electrochemical oscillators, impedance spectroscopy detects the Hopf bifurcations and the spiking regimes. We show that a neuron element needs three essential internal components: capacitor, inductor, and negative differential resistance. The method supports the fabrication of memristor-based artificial neural networks.
Highlights
The dynamics of neurons consist of oscillating patterns of a membrane potential that underpin the operation of biological intelligence
The resulting linear impedance data are described in terms of an equivalent circuit (EC) model that provides detailed information about the physical processes occurring at different time and frequency scales
To describe neuronal response and behavior, we adopt dynamical models formed by a nonlinear set of differential equations that emulate the actual output of a biological neuron.[24−26] Hodgkin and Huxley (HH) is a complete description of an excitable membrane by the concerted actuation of several ion channels, but it is computationally complex as it involves the membrane voltage and three different internal state variables
Summary
The dynamics of neurons consist of oscillating patterns of a membrane potential that underpin the operation of biological intelligence. The resulting linear impedance data are described in terms of an equivalent circuit (EC) model that provides detailed information about the physical processes occurring at different time and frequency scales.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
