Robust Synchronization of Time-Fractional Memristive Hopfield Neural Networks

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 $\alpha \in (0, 1)$.