Analysis of Stability in Rulkov Neural Networks with Fractional Orders and Asymmetric Memristor Synapses

Abstract

Fractional-order models effectively capture memory and hereditary effects in neural and nonlinear dy namical systems. Memristors are ideal components for modeling synaptic connections due to their ability to emulate plasticity and memory effects. Discrete models of memristor-coupled neurons simplify computa tions and enable efficient analysis of large-scale networks. Despite their potential, discrete fractional-order memristor-coupled models have been less explored. To address this, we propose two novel discrete fractional order neural systems. The first system is a two-neuron motif coupled via dual memristors, while the second extends this configuration to a ring-shaped network of similar subnetworks. A new theorem on the stabil ity of discrete fractional-order systems is established, defining stability regions for both models. Numerical simulations illustrate the theoretical results and investigate how the fractional order, asymmetric memristive coupling, and other model and network parameters jointly influence the dynamics and stability of discrete time neurons.