In this paper, cluster synchronization for fractional-order complex network with nondelay and delay coupling is investigated. Based on the stability theory of fractional-order systems and the properties of fractional derivative, both static and adaptive control schemes are adopted to design effective controllers. Sufficient condition for achieving cluster synchronization about static controllers is provided. From the condition, the needed feedback gains can be estimated by simple calculations. Further, adaptive control scheme is introduced to design unified controllers. Noticeably, in the adaptive controllers, the feedback gains need not be calculated in advance and can adjust themselves to the needed values according to updating laws. Finally, numerical simulations are given to demonstrate the correctness of the obtained results.

中文翻译：

---

非时延和时延耦合的分数阶网络中的簇同步

本文研究了具有无时延和时延耦合的分数阶复杂网络的簇同步问题。基于分数阶系统的稳定性理论和分数导数的性质，采用静态和自适应控制方案设计有效的控制器。为静态控制器实现集群同步提供了充分条件。根据该条件，可以通过简单的计算来估计所需的反馈增益。此外，引入自适应控制方案来设计统一控制器。值得注意的是，在自适应控制器中，反馈增益不需要预先计算，可以根据更新规律将自己调整到需要的值。最后通过数值模拟验证了所得结果的正确性。