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 dynamics due to the absence of equilibrium points, including bifurcation phenomena, coexisting attractors, transient chaos, state transitions, and offset-boosting control. Since equilibrium points are absent in this model, all observed dynamics are classified as hidden behaviors. The complex dynamics of this neuron model are illustrated through bifurcation diagrams, Lyapunov diagrams, time series plots, and phase portraits. Furthermore, an equivalent circuit for the memristor HR neuron is constructed, and the accuracy of numerical simulations is confirmed via circuit simulation results.