This article investigates the problem of exponential bipartite synchronization of fractional-order multilayer signed networks via hybrid impulsive control. First, the mathematical model of the networks is established by integrating the fractional dynamics of nodes, the multilayer network edges, and the positive and negative weights (antagonistic relationship), which is more pluralistic and practical. Second, a hybrid impulsive controller is designed, which is composed of the feedback control part and the impulsive control part to realize the exponential bipartite synchronization objective. Both positive and negative impulsive effects are considered and the ranges of the impulsive control gain related to the order of Caputo fractional derivative are discussed. In addition, some sufficient conditions for exponential bipartite synchronization of fractional-order multilayer signed networks are obtained by using the signed graph theory, Lyapunov method, and average impulsive interval method. Furthermore, in order to illustrate the practicability of the theoretical results, fractional-order coupled Chua’s circuits model and fractional-order power systems built on multilayer signed networks are established and the exponential bipartite synchronization issues are analyzed. Numerical examples and simulations are provided to show the effectiveness of the obtained results.

中文翻译：

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通过混合脉冲控制分数阶多层符号网络的指数二分同步


本文通过混合脉冲控制研究了分数阶多层符号网络的指数二部同步问题。首先，综合节点的分数动力学、多层网络边、正负权重（对抗关系）建立网络的数学模型，更加多元和实用。其次，设计了一种由反馈控制部分和脉冲控制部分组成的混合脉冲控制器，以实现指数二部同步目标。考虑了正脉冲效应和负脉冲效应，讨论了与Caputo分数阶导数阶数相关的脉冲控制增益范围。此外，利用符号图论、Lyapunov方法和平均脉冲区间方法，得到了分数阶多层符号网络指数二分同步的一些充分条件。此外，为了说明理论结果的实用性，建立了分数阶耦合蔡氏电路模型和基于多层符号网络的分数阶电力系统，并分析了指数二分同步问题。提供了数值例子和模拟来显示所获得结果的有效性。