Projective Synchronization Analysis of Fractional-Order Neural Networks With Mixed Time Delays

In this article, we analyze the projective synchronization of fractional-order neural networks with mixed time delays. By introducing an extended Halanay inequality that is applicable for the case of fractional differential equations with arbitrary initial time and multiple types of delays, sufficient criteria are deduced for ensuring the projective synchronization of fractional-order neural networks with both discrete time-varying delays and distributed delays. Furthermore, sufficient criteria are presented for ensuring the projective synchronization in the Mittag-Leffler sense if there is no delay in fractional-order neural networks. The results derived herein include complete synchronization, anti-synchronization, and stabilization of fractional-order neural networks as particular cases. Moreover, the testable criteria in this article are a meaningful extension of projective synchronization of neural networks with mixed time delays from integer-order to fractional-order ones. A numerical simulation with four cases is provided to verify the validity of the obtained results.