New conditions for synchronization in complex networks with multiple time-varying delays
New conditions for synchronization in complex networks with multiple time-varying delays
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DOI：
10.1016/j.cnsns.2013.01.006
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发表时间：
2013-09
期刊：
影响因子：
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通讯作者：
Yan Dong;Jinguo Xian;D. Han
中科院分区：
文献类型：
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作者：
Yan Dong;Jinguo Xian;D. Han
本文研究了两类具有多个时变时滞的复杂动态网络的同步问题，即具有固定拓扑结构和具有切换拓扑结构的情况。对于前者，不同于通常使用的线性矩阵不等式（LMI）方法，我们采用了基于网络加权邻接矩阵置乱特性的方法。研究结果表明，如果网络的加权邻接矩阵具有置乱特性，且耦合强度足够大，则在适当的通信时延下，网络将实现指数同步.请注意，我们的同步条件是非常新的，这将是很容易检查与以前报告的LMI相比。此外，我们将结果推广到相互作用拓扑是切换的情况。在每种情况下，通信延迟的最大允许上界。数值仿真结果验证了理论结果的有效性。
In this paper, two kinds of synchronization problems of complex dynamical networks with multiple time-varying delays are investigated, that is, the cases with fixed topology and with switching topology. For the former, different from the commonly used linear matrix inequality (LMI) method, we adopt the approach basing on the scramblingness property of the network’s weighted adjacency matrix. The obtained result implies that the network will achieve exponential synchronization for appropriate communication delays if the network’s weighted adjacency matrix is of scrambling property and the coupling strength is large enough. Note that, our synchronization condition is very new, which would be easy to check in comparison with those previously reported LMIs. Moreover, we extend the result to the case when the interaction topology is switching. The maximal allowable upper bounds of communication delays are obtained in each case. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.