BIFURCATION ANALYSIS OF A NFDE ARISING FROM MULTIPLE-DELAY FEEDBACK CONTROL

被引：7
|
作者：
Niu, Ben [1 ,2 ]
Wei, Junjie [1 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
[2] Harbin Univ Sci & Technol, Dept Appl Math, Harbin 150080, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2011年 / 21卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Amplitude equation; neutral type; Hopf bifurcation; periodic solution; FUNCTIONAL-DIFFERENTIAL EQUATIONS; HOPF-BIFURCATION; NORMAL FORMS; STABILITY; PARAMETERS; NETWORK; SYSTEM; CHAOS; MODEL;
D O I：
10.1142/S0218127411028775
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the stability and Hopf bifurcation of a neutral functional differential equation (NFDE) which is transformed from an amplitude equation with multiple-delay feedback control. By analyzing the distribution of the eigenvalues, the stability and existence of Hopf bifurcation are obtained. Furthermore, the direction and stability of the Hopf bifurcation are determined by using the center manifold and normal form theories for NFDEs. Finally, we carry out some numerical simulations to illustrate the results.
引用
收藏
页码：759 / 774
页数：16
相关论文
共 50 条
  • [1] Laser stabilization with multiple-delay feedback control
    Ahlborn, A
    Parlitz, U
    [J]. OPTICS LETTERS, 2006, 31 (04) : 465 - 467
  • [2] Multiple bifurcation analysis in a NDDE arising from van der Pol's equation with extended delay feedback
    Niu, Ben
    Jiang, Weihua
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (01) : 699 - 717
  • [3] On multiple-delay output feedback stabilization of LTI plants
    Roy, Sandip
    Saberi, Ali
    Wan, Yan
    [J]. INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2010, 20 (11) : 1299 - 1305
  • [4] On multiple-delay static output feedback stabilization of LTI plants
    Roy, Sandip
    Saberi, Ali
    Wan, Yan
    [J]. 2008 AMERICAN CONTROL CONFERENCE, VOLS 1-12, 2008, : 419 - 423
  • [5] Bifurcation analysis in the control of chaos by extended delay feedback
    Guo, Yuxiao
    Jiang, Weihua
    Niu, Ben
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2013, 350 (01): : 155 - 170
  • [6] Regularized Kernel Least Mean Square Algorithm with Multiple-delay Feedback
    Wang, Shiyuan
    Zheng, Yunfei
    Ling, Chengxiu
    [J]. IEEE SIGNAL PROCESSING LETTERS, 2016, 23 (01) : 98 - 101
  • [7] Bifurcation analysis in active control system with time delay feedback
    Peng, Jian
    Wang, Lianhua
    Zhao, Yueyu
    Zhao, Yaobing
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (19) : 10073 - 10081
  • [8] Bounded control of multiple-delay systems with applications to ATM networks
    Tarbouriech, S
    Abdallah, CT
    Ariola, M
    [J]. PROCEEDINGS OF THE 40TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5, 2001, : 2315 - 2320
  • [9] Nonlinear Multiple-Delay Feedback Based Kernel Least Mean Square Algorithm
    Zhao, Ji
    Liu, Jiaming
    Li, Qiang
    Tang, Lingli
    Zhang, Hongbin
    [J]. NEURAL INFORMATION PROCESSING, ICONIP 2023, PT I, 2024, 14447 : 118 - 129
  • [10] Combination of sign inverting and delay scheduling control concepts for multiple-delay dynamics
    Gao, Qingbin
    Kammer, Ayhan S.
    Zalluhoglu, Umut
    Olgac, Nejat
    [J]. SYSTEMS & CONTROL LETTERS, 2015, 77 : 55 - 62
12345