IEEE Trans Cybern. 2022 Jul;52(7):6798-6808. doi: 10.1109/TCYB.2020.3027755. Epub 2022 Jul 4.
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.
在本文中，我们分析了具有混合时滞的分数阶神经网络的投影同步。通过引入一个适用于具有任意初始时间和多种类型延迟的分数微分方程的扩展 Halanay 不等式，推导出了充分条件，以确保具有离散时变延迟和分布式延迟的分数阶神经网络的投影同步。此外，如果分数阶神经网络中没有延迟，则给出了在 Mittag-Leffler 意义上的投影同步的充分条件。本文得到的结果包括分数阶神经网络的完全同步、反同步和稳定化作为特例。此外，本文中的可测试准则是将具有混合时滞的神经网络的投影同步从整数阶扩展到分数阶的一个有意义的扩展。通过四个案例的数值模拟验证了所得到的结果的有效性。
