A threshold effect of coupling delays on intra-layer synchronization in duplex networks

作     者：TANG LongKun LU JunAn Lü JinHu 

作者机构：Fujian Province University Key Laboratory of Computation Science School of Mathematical Sciences Huaqiao University Department of Mathematics & Statistics Georgia State University School of Mathematics and Statistics Wuhan University School of Automation Science and Electrical Engineering State Key Laboratory of Software Development Environment and Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University 

出 版 物：《Science China(Technological Sciences)》 (中国科学（技术科学英文版）)

年 卷 期：2018年第61卷第12期

页      面：1907-1914页

核心收录：

学科分类：08[工学] 0802[工学-机械工程] 

基　　金：supported by the National Key Research and Development Program of China (Grant No. 2016YFB0800401) the National Natural Science Foundation of China (Grant Nos. 61621003, 61532020, 61573262, 61573004) the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (Grant No. ZQNYX301, ZQN-PY401) the Natural Science Foundation of Fujian Province (Grant Nos. 2015J01260, 2015J01584) the Program for New Century Excellent Talents in Fujian Province University in 2016 the Cultivation Program for Outstanding Young Scientific Talents of the Higher Education Institutions of Fujian Province in 2016 

主　　题：multiplex network master stability function intra-layer synchronization synchronized region time delay 

摘      要：This paper investigates the impact of inter-layer coupling functions and intra-layer coupling delays on intra-layer synchronization regions and sychronizability. It is found that the inter-layer coupling functions have great influence on intra-layer synchronization regions, as well as on the intra-layer synchronizability. In particular, there exists an inter-layer coupling function such that the inter-layer coupling strength neither improves nor weakens the intra-layer synchronizability. Furthermore, no matter which one of three inter-layer coupling functions is chosen, a small intra-layer delay always keeps the intra-layer synchronized regions almost unchanged, implying that the small delay neither enhances nor suppresses the intra-layer synchronizability. At the same time the delay greatly frustrates the synchronizability in each layer when it is greater than some threshold. Our results may have potential applications for interconnected technological networks where communication delays are inevitably present.