This article is devoted to the cluster synchronization issue of coupled fractional-order neural networks. By introducing the stability theory of fractional-order differential systems and the framework of Filippov regularization, some sufficient conditions are derived for ascertaining the asymptotic and finite-time cluster synchronization of coupled fractional-order neural networks, respectively. In addition, the upper bound of the settling time for finite-time cluster synchronization is estimated. Compared with the existing works, the results herein are applicable for fractional-order systems, which could be regarded as an extension of integer-order ones. A numerical example with different cases is presented to illustrate the validity of theoretical results.

中文翻译：

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时滞耦合分数阶神经网络的渐近有限时间簇同步


本文致力于耦合分数阶神经网络的簇同步问题。通过引入分数阶微分系统稳定性理论和Filippov正则化框架，分别推导了确定耦合分数阶神经网络渐进和有限时间簇同步的充分条件。此外，还估计了有限时间集群同步的稳定时间的上限。与现有工作相比，本文的结果适用于分数阶系统，可以看作是整数阶系统的扩展。给出了不同情况下的数值例子来说明理论结果的有效性。