具有双重时滞的时变耦合复杂网络的牵制外同步研究

Outer synchronization analysis of two time-varying networks with double delays based on pinning control

针对同时具有节点时滞和耦合时滞的时变耦合复杂网络的外同步问题,提出一种简单有效的自适应牵制控制方法.首先构建一种贴近实际的驱动-响应复杂网络模型,在模型中引入双重时滞和时变不对称外部耦合矩阵.进一步设计易于实现的自适应牵制控制器,对网络中的一部分关键节点进行控制.构造适当的Lyapunov泛函,利用La Salle不变集原理和线性矩阵不等式,给出两个复杂网络实现外同步的充分条件.最后,仿真结果表明所提同步方法的有效性,同时揭示耦合时滞对同步收敛速度的影响.

It is well known that time delay is universal in complex networks. However, in most existing researches outer synchronization is realized between two networks with time delay by adding controllers to all nodes which may bring great economic costs and increase the difficulties in control in practice. In this paper, in order to deal with the problem of outer synchronization between two time-varying coupling networks with node delay and coupling delay, an adaptive pinning control scheme is proposed. First, a more realistic drive-response complex network model is constructed by introducing double delays and asymmetric coupling configuration matrices. Then, we design an adaptive pinning controller which is easy to implement, and choose an effective pinning strategy to control a crucial part of the nodes in the response network. Based on La Salle＇ invariance principle and the linear matrix inequality, we may rigorously prove that the outer synchronization between the proposed drive-response networks can be achieved, and meanwhile some sufficient conditions are derived by adopting an appropriate Lyapunov-Krasovskii energy function. Finally, numerical simulation experiments are employed to verify the correctness and the effectiveness of the proposed method. Results indicate that the drive-response networks with double delays can indeed achieve outer synchronization by pinning control. Moreover, the synchronization is independent of coupling delay. And the remarkable influences of coupling delays on the synchronization speed are also revealed.