Robust Synchronization of Time-Fractional Memristive Hopfield Neural Networks

We introduce and study robust synchronization of time-fractional Hopfield neural networks with memristive synapses and Hebbian learning. This novel model of artificial neural networks exhibits strong memory and long-range path dependence. By scaled group estimates and analysis of fractional differencing equations, it is proved that under rather general assumptions the solution dynamics are globally dissipative and there exists a threshold condition for achieving robust synchronization of the entire neural networks if this condition is satisfied by the interneuron coupling strength. The synchronizing threshold is explicitly expressed in terms of the original parameters in the model equations and strictly decreasing for the fractional order $\alpha \in (0,1)$. This result makes a breakthrough in the exploration of fractional global and longtime dynamics for AI mathematical models.