Dynamics of a Hindmarsh–Rose neuron with dual memristive inputs: Electromagnetic flux and autapse feedback

In neurological systems, autapses-synaptic connections in neurons—are recognized for their impact on excitability, firing patterns, and information processing within brain systems. In this study, we propose a novel extension of the Hindmarsh–Roseneuron model by incorporating two distinct memristive mechanisms, resulting in a dual-memristor system. The first memristor represents the influence of an external electromagnetic field, implemented as a fast, oscillatory cosine-based current to capture transient external perturbations. The second memristor emulates an activity-dependent autapse, modeled as a slow, saturating feedback current governed by a hyperbolic tangent function, reflecting the cumulative nature of synaptic adaptation. Each memristor evolves according to an internal state variable, allowing for the joint representation of intrinsic feedback and extrinsic stimulation within a unified dynamical framework. To analyze the dynamics of the proposed dual-memristive HR neuron model, we perform a stability analysis of the equilibrium points and utilize bifurcation diagrams alongside Lyapunov exponents to investigate parameter-dependent transitions inside the system. Additionally, interspike interval statistics — specifically, the coefficient of variation (CV), skewness (SK) and burst ratio (BR) — are used to quantify the regularity and bursting nature of the firing patterns. Numerical simulations reveal that this combined mechanism significantly enriches the dynamical repertoire of the neuron, causing irregular spiking, burst, and chaotic regimes.