📝 SummarXiv

Abstract

Memristors have emerged as ideal components for modeling synaptic connections in neural networks due to their ability to emulate synaptic plasticity and memory effects. Discrete models of memristor-coupled neurons are crucial for simplifying computations and efficiently analyzing large-scale neural networks. Furthermore, incorporating fractional-order calculus into discrete models enhances their capacity to capture the memory and hereditary properties inherent in biological neurons, thus reducing numerical discretization errors compared to integer-order models. Despite this potential, discrete fractional-order neural models coupled through memristors have received limited attention. To address this gap, we introduce two novel discrete fractional-order neural systems. The first system consists of two Rulkov neurons coupled via dual memristors to emulate synaptic functions. The second system expands this configuration into a ring-shaped network of neurons consisting of multiple similar subnetworks. We present a novel theorem that defines stability regions for discrete fractional-order systems, applicable to both proposed models. Integrating discrete fractional-order calculus into memristor-coupled neural models provides a foundation for more accurate and efficient simulations of neural dynamics. This work advances the understanding of neural network stability and paves the way for future research into efficient neural computations.