Exploring the Influence of Synaptic Parasitic Resistance on the Firing Dynamics of Memristor-Based HR-Tabu Neural Network

Neural circuits are inevitably exposed to ubiquitous interference sources, which gives rise to parasitic resistance. This phenomenon has profound yet largely unexplored effects on neuronal firing dynamics and overall circuit performance, highlighting a critical gap in our understanding. To address this gap, this paper investigates the influence of parasitic resistance on the firing dynamics of memristor-based neural networks from a nonlinear dynamics perspective. Firstly, we propose a composite multi-stable memristor that incorporates a series resistor to emulate the effect of synaptic parasitic resistance. Subsequently, we conduct a systematic analysis of this effect utilizing nonlinear circuit theory, with particular focus on the equilibrium point evolution within a composite memristor synapse-based neural network (CMS-NN) that comprises of a Hindmarsh-Rose (HR) neuron and a tabu neuron. Our results demonstrate that an increase of series resistor slows down both the speed and distance of equilibrium point shifts in the multi-stable memristor, leading to simpler equilibrium distribution and decelerated dynamical evolution of CMS-NN. Thus, this mechanism enables the regulation of firing patterns and synchronization behaviors of CMS-NN, which is expectedly confirmed by numerical simulations and circuit experiments. As the first demonstration of parasitic resistance being harnessed for neural activity modulation, this work not only enhances the fundamental understanding of neural dynamics but also provides a practical design framework for memristor-based neuromorphic circuits.