This paper is concerned with the existence of periodic solutions for feedback control coupled systems on networks (FCCSNs) by a novel approach, which is made up of the continuation theorem of coincidence degree theory, graph theory, Lyapunov method, and some novel analysis skills. As an application of our approach, the existence and global asymptotic stability of periodic solutions for feedback control coupled oscillators on networks are investigated. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of our results.

中文翻译：

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网络上反馈控制耦合系统的周期性解决方案

本文通过一种新颖的方法关注网络上反馈控制耦合系统（FCCSNs）周期解的存在，该方法由重合度理论的连续定理、图论、Lyapunov方法和一些新颖的分析技巧组成。作为我们方法的一种应用，研究了网络上反馈控制耦合振荡器的周期性解的存在性和全局渐近稳定性。最后，通过数值模拟来说明我们结果的有效性和可行性。