Revelation and experimental verification of quasi-periodic bursting, periodic bursting, periodic oscillation in third-order non-autonomous memristive FitzHugh-Nagumo neuron circuit

Abstract

It has been declared that constructing physical hardware circuits with the reproduction of abundant electrical activities of neurons is significant in neuron-based engineering applications. To this end, a novel third-order non-autonomous memristive FitzHugh-Nagumo (FHN) neuron circuit is designed by employing a first-order generalized memristive-diode-bridge (MDB) emulator and an AC voltage source. The memristive FHN neuron circuit can generate abundant electrical activities since the involvement of the MDB emulator. In theoretical analysis and numerical simulation, the corresponding circuit state equations and normalized system are formulated to analyze the characteristics of the equilibrium point and investigate the dynamical behaviors related to the internal resistor of the MDB emulator. Then phase portrait, time-domain waveform, bifurcation diagram, and Lyapunov exponent spectra are numerically simulated, from which abundant non-chaotic firing activities of quasi-periodic bursting, periodic bursting, and periodic oscillation are revealed. Additionally, the 0–1 test is utilized to further distinguish the above three non-chaotic behaviors. In hardware experiment, a breadboard hardware circuit is constructed and experimental measurements are executed. It is demonstrated that the experimental results well support the numerical simulations. Studying these non-chaotic behaviors is very important to understand the intrinsic nature of neuronal firing activities. Most notably, the numerical revelation and experimental verification of quasi-periodic bursting behavior have been rarely reported in the previously published literature.