Pinning synchronization of complex networks with two different kinds of time-varying coupling are studied in this paper. Inner coupling of the state variables and outer coupling in the complex network are taken into consideration. Based on the Lyapunov function theory, some general criteria and a simplified corollary for ensuring network synchronization are proposed. Linear pinning controllers, adaptive pinning controllers and adaptive coupling strength are designed for achieving complex network time-varying synchronization. Furthermore, the analytic relationship between control parameters is studied. Numerical simulations further illustrate the effectiveness of conclusions.

中文翻译：

---

基于自适应钉扎控制的时变耦合复杂网络同步

本文研究了具有两种不同时变耦合的复杂网络的钉扎同步。考虑了复杂网络中状态变量的内耦合和外耦合。基于Lyapunov函数理论，提出了保证网络同步的一般准则和简化推论。线性钉扎控制器、自适应钉扎控制器和自适应耦合强度被设计用于实现复杂的网络时变同步。此外，研究了控制参数之间的解析关系。数值模拟进一步说明了结论的有效性。