Dynamical Analysis and Circuit Implementation of HR-FHN Neuron Model Coupled by Locally Active Memristor

In this paper, a novel locally active memristor is constructed. Based on the 3D Hindmarsh–Rose (HR) and 2D FitzHugh–Nagumo (FHN) neuron, a heterogeneous neuronal system is constructed by connecting the two neurons with the locally active memristor. The equilibrium point and stability of the system are investigated. The dynamic behavior of the system is numerically and experimentally revealed by utilizing dynamic analyses in terms of interspike interval bifurcation diagram, two-parameter bifurcation diagram and so on. The unique and abundant dynamic behavior is found in the proposed neuronal system by varying the coupling strength, external stimulus current, memristive parameter and other system parameters. Multiple bursting firing groups in the tongue-shaped domains have been discovered for the first time. Finally, in order to validate the numerical simulation, an analog equivalent circuit of the heterogeneous neuronal system is devised, which demonstrates that the system is physically realizable.