Memristive Effect on a Hindmarsh-Rose Neuron

Considering the impact of electromagnetic induction on neurons, this paper presents a three-dimensional (3D) memristor Hindmarsh-Rose (HR) neuron model. This model exhibits diverse hidden chaotic dynamic behaviors due to the absence of equilibrium points, including bifurcation phenomena, coexisting attractors, transient chaos, state transitions, and offset-boosting control. As equilibrium points are absent in this model, all generated dynamics represent hidden behaviors. The intricate dynamics of this neuron model are elucidated through bifurcation diagrams, Lyapunov diagrams, time series plots, and phase portraits. Furthermore, an equivalent circuit for this memristor HR neuron is devised and the correctness of numerical simulations is validated via circuit simulation results.