Hybrid Control of Delay Induced Hopf Bifurcation of Dynamical Small-World Network

作     者：丁大为 张肖芸 王年 梁栋 

作者机构：Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Electronics and Information Engineering Anhui University 

出 版 物：《Journal of Shanghai Jiaotong university(Science)》 (上海交通大学学报（英文版）)

年 卷 期：2017年第22卷第2期

页      面：206-215页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0701[理学-数学] 071101[理学-系统理论] 0811[工学-控制科学与工程] 

基　　金：the National Natural Science Foundation of China(Nos.61201227 and 61172127) the Natural Science Foundation of Anhui(No.1208085MF93) 

主　　题：Hopf bifurcation hybrid control small-world network bifurcation control 

摘      要：In this paper, we focus on the Hopf bifurcation control of a small-world network model with time-delay. With emphasis on the relationship between the Hopf bifurcation and the time-delay, we investigate the effect of time-delay by choosing it as the bifurcation parameter. By using tools from control and bifurcation theory, it is proved that there exists a critical value of time-delay for the stability of the model. When the time-delay passes through the critical value, the model loses its stability and a Hopf bifurcation occurs. To enhance the stability of the model, we propose an improved hybrid control strategy in which state feedback and parameter perturbation are used. Through linear stability analysis, we show that by adjusting the control parameter properly, the onset of Hopf bifurcation of the controlled model can be delayed or eliminated without changing the equilibrium point of the model. Finally, numerical simulations are given to verify the theoretical analysis. © 2017, Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg.