On Hopf bifurcation and control for a delay systems

被引：31

作者：

Jiang, Xiaowei ^{[1
,3
,4
]}

Chen, Xiangyong ^{[2
]}

Chi, Ming ^{[3
]}

Chen, Jie ^{[5
]}

机构：

[1] China Univ Geosci, Sch Automat, Wuhan 430074, Hubei, Peoples R China

[2] Linyi Univ, Sch Automat & Elect Engn, Linyi 276005, Shandong, Peoples R China

[3] Hubei Key Lab Adv Control & Intelligent Automat C, Wuhan 430074, Hubei, Peoples R China

[4] Hubei Normal Univ, Coll Mechatron & Control Engn, Huangshi 435002, Hubei, Peoples R China

[5] Hubei Univ Technol, Sch Sci, Wuhan 430068, Hubei, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 370卷

基金：

中国国家自然科学基金;

关键词：

Hopf bifurcation; Time lag; Stability; Bifurcation control; NEIMARK-SACKER BIFURCATION; STABILITY; EQUATIONS; NETWORKS; MODEL;

D O I：

10.1016/j.amc.2019.124906

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Hopf bifurcation of a delay differential equation modeling two-enterprise interaction mechanism is investigated. For the demands of computer simulation applications, the discrete-time two-enterprise interaction model is proposed by using the forward Euler scheme. By discussing the characteristic equation of linearized part, the local stability criterion of the positive fixed point is presented. Time lag is selected as the bifurcation parameter. Then it is demonstrated that variation of time lag may result in Hopf bifurcation. Furthermore, derivations for the directions and stability of Hopf bifurcation are also given. For the purpose of controlling Hopf bifurcation, a time-delayed feedback control scheme is proposed. Finally, we simulate the main results. (C) 2019 Elsevier Inc. All rights reserved.

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