A hybrid intelligent computational framework for diverse firing patterns in a fractional-order Locally Active Memristive Neuron model

Memristive neuronal architectures constitute sophisticated dynamical systems that exhibit complex nonlinear spiking phenomena through the synergistic integration of memory-dependent conductance modulation and intrinsic neuronal dynamics. This investigation elucidates the emergent behavioral manifestations of a Locally Active Memristive Neuron (LAMfrefeN) paradigm, synthesized through the amalgamation of a two-dimensional Hindmarsh-Rose neuronal substrate with an autaptic memristive element exhibiting locally active characteristics. In this paper, this dynamical framework undergoes systematic transformation into a fractional-order paradigm through the rigorous implementation of the Caputo fractional differential operator, namely the Fractional Locally Active Memristive Neuron (FLAMN) model. Numerical integration of the Fractional-order system is accomplished via the Adams-Bashforth-Moulton Predictor-Corrector (FABM-PrCr) computational methodology. Fractional-order derivatives inherently incorporate non-local hereditary memory effects, substantially enhancing the system's representational fidelity in capturing the intricate temporal dynamics and long-range dependencies characteristics of biological neurons. The proposed FLAMN configuration demonstrates quintessential neuronal excitability patterns encompassing periodic bursting, periodic spiking, chaotic bursting, chaotic bursting and stochastic bursting firing regimes, thereby recapitulating the multifaceted electrophysiological repertoire observed in biological neural architectures. Subsequently, an intelligent computational framework is designed to function as a sophisticated surrogate system for the FLAMN model, by means of a Hybrid Non-Linear AutoRegressive Neural Network backpropagated through Levenberg-Marquardt (HNLARXNN-LM) algorithm. The forecasting and modeling prowess of the diverse firing patterns of the FLAMN is done through diverse error analysis on singular and multi-step ahead horizons, error histogram, correlation and regression analysis. Empirical results demonstrate mean squared errors in the ranges of 10−9–10−11. The FLAMN dynamical systems reconstruction by NLARXNN is visually apprehended through comparative time-series and absolute error evolution curves. With reconstruction error as low as 10−3–10−6, we showcase that the developed FLAMN framework demonstrates exceptional consistency in reproducing the intricate temporal dynamics and statistical properties of the memristive neuron, establishing a robust foundation for subsequent investigations into neuromorphic computing applications and theoretical neuroscience endeavors. An inference study on completely unseen FitzHugh-Nagumo spiking dynamics further validates this claim, with reconstruction errors in the ranges of 10−5 to 10−7, showcasing apt cross-generalizability and effectiveness of the HNLARXNN-LM as a surrogate differential solver.