Improving dynamics of integer-order small-world network models under fractional-order PD control
Improving dynamics of integer-order small-world network models under fractional-order PD control作者机构：College of Automation Nanjing University of Posts and Telecommunications School of Mathematics and Physics Qingdao University of Science and Technology College of Science Nanjing University of Posts and Telecommunications School of Mathematics and Statistics Xinyang Normal University School of Automation and Electrical Engineering Linyi University
出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))
年 卷 期：2020年第63卷第1期
页 面：200-212页
核心收录：
学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070104[理学-应用数学] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071102[理学-系统分析与集成] 081103[工学-系统工程]
基 金：supported in part by National Natural Science Foundation of China (Grant Nos. 61573194, 51775284, 61877033) Natural Science Foundation of Jiangsu Province of China (Grant Nos. BK20181389, BK20181387) Key Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province (Grant No. 2018SJZDI142) Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX18 0924)
主 题：small-world networks stability Hopf bifurcation bifurcation control fractional-order PD control
摘 要：The optimal control of dynamics is a popular topic for small-world networks. In this paper, we address the problem of improving the behavior of Hopf bifurcations in an integer-order model of small-world networks. In this study, the time delay is used as the bifurcation parameter. We add a fractional-order proportional-derivative(PD) scheme to an integer-order Newman-Watts(N-W) small-world model to better control the Hopf bifurcation of the model. The most important contribution of this paper involves obtaining the stability of the system and the variation of the conditions of the Hopf bifurcation after a fractional PD controller is added to the integer-order small-world model. The results demonstrate that the designed PD controller can be used to restrain or promote the occurrence of Hopf bifurcations by setting appropriate parameters. We also describe several simulations to verify our research results.
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