Eur. Phys. J. Spec. Top. (2021) 230: 1751-1762
https://doi.org/10.1140/epjs/s11734-021-00121-0

Regular Article

Dynamical analysis in dual-memristor-based FitzHugh–Nagumo circuit and its coupling finite-time synchronization

School of Electrical and Automation Engineering, Nanjing Normal University, 210023, Nanjing, China

^b minfuhong@njnu.edu.cn

Received: 19 September 2020
Accepted: 28 April 2021
Published online: 18 June 2021

Abstract

This paper presents an improved dual-memristor-based FitzHugh–Nagumo (DM-FHN) system, which is a non-autonomous circuit derived from FitzHugh–Nagumo (FHN) neuron circuit by substituting the tunnel diode with hyperbolic tangent memductance and connecting an active charge-controlled memristor in series with an inductor. The analysis model of the system is established first, and the rich dynamic behaviors of the system, varying with the circuit component parameters, are studied via the phase diagram, bifurcation diagram and Lyapunov exponential spectrum. Some interesting phenomena, such as bifurcation, periodic-chaotic state transition, periodic-chaotic bubbles, multistability phenomenon, and symmetrical behaviors, are observed. The finite-time synchronization of two coupled DM-FHN neurons for different behaviors due to different initial conditions is also studied. The cubic flux-controlled memristor is used as a synapse between the coupling circuits. The sufficient synchronization conditions for the unidirectional and bidirectional coupling DM-FHN circuits are derived respectively and the influence of the system initial values on the coupling synchronization is also investigated. The rich synchronous dynamics of the coupled DM-FHN systems are illustrated by the numerical simulations, the result of which also validates the presented analysis model.