College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China.
Neural Netw. 2024 Apr;172:106124. doi: 10.1016/j.neunet.2024.106124. Epub 2024 Jan 12.
In this paper, we consider the exponential bipartite synchronization (EBS) problem of fractional-order multilayer signed networks with time-varying delays (FO-MSNT) under random cyber attacks. In contrast to the existing literature, the proposed hybrid event-triggered controller combines the advantages of feedback controller and impulsive controller, and the event-triggered condition is constructed by applying the network topology and the Lyapunov function of the subsystem, rather than the state function of the subsystem. Based on the Lyapunov-Razumikhin method and the graph theory, some sufficient conditions for achieving EBS of FO-MSNT under cyber attacks which are related to the topology of networks, the event-triggered parameters, the order of fractional derivative and the signal sent by the enemy are obtained. Furthermore, fractional-order coupled Chua's circuits model and fractional-order power systems built on MSNT are established and the EBS issues under cyber attacks are analyzed. Numerical examples and simulations are provided to show the validity of our theories.
本文研究了具有时变时滞的分数阶多层有向网络（FO-MSNT）在随机网络攻击下的指数二分同步（EBS）问题。与现有文献相比，所提出的混合事件触发控制器结合了反馈控制器和脉冲控制器的优点，并且事件触发条件是通过应用网络拓扑和子系统的李雅普诺夫函数构建的，而不是子系统的状态函数。基于李雅普诺夫-拉兹米金方法和图论，得到了在网络拓扑、事件触发参数、分数阶导数阶数和敌方发送信号等与网络攻击相关的条件下，实现 FO-MSNT 的 EBS 的充分条件。此外，建立了基于 MSNT 的分数阶耦合蔡氏电路模型和分数阶电力系统，并分析了网络攻击下的 EBS 问题。提供了数值示例和仿真结果以验证我们理论的有效性。
