In this paper, we consider 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, Kirchhoff’s matrix tree theorem in graph theory, Lyapunov
method, and some 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, an example and its numerical simulations are given to
illustrate the effectiveness and feasibility of our results.