Coupled HR–HNN Neuron with a Locally Active Memristor

Local activity could be the source for complexity. In this study, a multistable locally active memristor is proposed, whose nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC $V$–$I$ plot. Based on the two-dimensional Hindmarsh–Rose neuron and a one-dimensional Hopfield neuron, a simple neural network is constructed by connecting the two neurons with the locally active memristor. Coexisting multiple firing patterns under different initial conditions are investigated according to the controlled coupling factor. The results suggest that the system exhibits coexisting periodic and chaotic bursting with different firing patterns. Complex firing only occurs in the locally active area of the defined memristor, meanwhile the system shows a periodic oscillation in the passive area. Beyond this, the coupled neurons exhibit the specific phenomenon of attractor growing in the locally active region of the memristor. The circuit simulations by Power Simulation (PSIM) are included confirming the numerical simulations and theoretic analysis.