Robust Synchronization of Time-Fractional Memristive Hopfield Neural Networks
Yuncheng You
TL;DR
The paper develops a rigorous framework for robust synchronization in Caputo time-fractional memristive Hopfield networks with Hebbian learning. By proving global dissipativity and an absorbing ball with radius $M(\alpha)$, it obtains explicit, computable synchronization thresholds $P_\alpha^*(\varepsilon)$ that guarantee $\deg_s(\mathcal{NW}) < \varepsilon$ when the interneuron coupling $P$ exceeds the threshold. The threshold is shown to decrease with the fractional order $\alpha$, indicating memory effects influence convergence rates, which follow a fractional power-law $O([\mu t^\alpha]^{-1})$ rather than exponential decay. The results provide concrete design criteria for achieving robust synchronization in fractional memristive neural networks and offer a pathway to extensions in multilayer or multiplex architectures.
Abstract
In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range path-dependence in learning processes. Through scaled group estimates it is proved that under rather general assumptions the solution dynamics is globally dissipative. The main result established a threshold condition for achieving robust synchronization of the neural networks if it is satisfied by the interneuron coupling strength coefficient. The synchronizing threshold is explicitly computable in terms of the original parameters and strictly decreasing for the fractional order $α\in (0, 1)$.