Characterizing emergent firing-pattern diversity in an autaptic neuron with second-order memristive synapse

The locally active memristor (LAM), deemed an ideal building block for neuromorphic computing due to its signal amplification and oscillation sustainment capabilities, inspires the proposal of a novel second-order locally active memristor (SOLAM). The electrical properties of the SOLAM are examined via a quantitative approach leveraging small-signal analysis in conjunction with the theory of local activity. Utilizing the SOLAM, this work develops a second-order memristive autapse Hindmarsh–Rose (SOMAHR) model, which accurately captures the complex dynamics of the neuron under electromagnetic radiation (EMR) and uncovers the existence of multiple distinct firing patterns, and the physical realizability of the SOMAHR model was confirmed through the construction of an analog circuit. To further probe the firing patterns of the SOMAHR, an additional state-dependent stimulus is incorporated, yielding the SOMAHR-S. Numerical analysis reveals that tuning the frequency of this stimulus enables precise control over unique firing patterns, which manifest as multiscroll chaotic attractors with complexity governed by the stimulus frequency. Remarkably, this gives rise to a regime of infinite heterogeneous coexisting attractors, a phenomenon of particular interest for multistable systems.