中文摘要：

在目前已有的复杂网络模型的基础上,给出了一类混合变时滞二重边复杂网络模型,它不仅包含2个不同性质的子网络,而且同时含有节点时滞和耦合时滞,且2种时滞都随时间而变化。基于Lyapunov-Krasovskii泛函方法,在一些保守性较小的假设和对网络参数要求很弱的情况下,运用合适的不等式放缩,分别给出了混合变时滞二重边复杂网络渐近同步和指数同步的自适应反馈控制器设计方法。实例数值仿真结果说明了控制方法的有效性,并通过取相同初始值,验证了网络在指数同步控制器控制下同步速度更快。

英文摘要：

Based on current complex network models,a new and general double-linked complex network with time-varying delayed nodes and couplings was introduced.This model not only contains two sub-networks of different natures but also delayed nodes and couplings,and the two types of delays are both time-varying.Via the Lyapunov-Krasovskii functional method,under smaller conservative assumption and weaker requirements of the network parameters,the adaptive feedback controllers of the complex network for asymptotic synchronization and exponential synchronization were designed by using inequality.The results of numerical calculation show the effectiveness of the control methods.By giving the same initial value,it is verified that the synchronous speed of the network under exponentially synchronous control is faster.