Hopf bifurcation analysis for genetic regulatory networks with two delays

被引：26
|
作者：
Yu, Tingting [1 ]
Zhang, Xian [2 ]
Zhang, Guodong [2 ]
Niu, Ben [3 ]
机构：
[1] Harbin Inst Technol, Space Control & Inertial Technol Res Ctr, Harbin 150080, Peoples R China
[2] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Peoples R China
[3] Harbin Inst Technol Weihai, Dept Math, Weihai 264200, Peoples R China
来源：
NEUROCOMPUTING | 2015年 / 164卷
基金：
中国国家自然科学基金;
关键词：
Delay; Hopf bifurcation; Stability; Genetic regulatory networks; NEURAL-NETWORK; EXPONENTIAL STABILITY; SWITCHING PARAMETERS; MODEL; OSCILLATIONS; EQUATION; SYSTEMS;
D O I：
10.1016/j.neucom.2015.02.070
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, a genetic regulatory network with two time delays is considered. Firstly, the stabilities with one delay and two delays are investigated. It is shown that the stability switches for time delays, and Hopf bifurcation may occur within certain range of the model parameters. Then, combining the normal form method and the center manifold theorem, we derive the explicit formulas which determine the direction of the bifurcation and the stability of the bifurcated periodic solutions. Finally, some numerical examples are exploited to support our results. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码：190 / 200
页数：11
相关论文
共 50 条
  • [1] Stability and Hopf Bifurcation of Genetic Regulatory Networks with Multiple Delays
    Chen, Gang
    Xiao, Min
    Jiang, Guo-Ping
    2015 27TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC), 2015, : 2454 - 2459
  • [2] Stability and Bifurcation of Genetic Regulatory Networks with Delays
    Liu Feng
    Xiong Gaoxiang
    Yang Chao
    Guan Zhi-Hong
    Wang Hua O
    2014 33RD CHINESE CONTROL CONFERENCE (CCC), 2014, : 2244 - 2248
  • [3] Stability and bifurcation of genetic regulatory networks with delays
    Wang, Kai
    Wang, Lei
    Teng, Zhidong
    Jiang, Haijun
    NEUROCOMPUTING, 2010, 73 (16-18) : 2882 - 2892
  • [4] Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays
    Xiao, Min
    Cao, Jinde
    MATHEMATICAL BIOSCIENCES, 2008, 215 (01) : 55 - 63
  • [5] Bifurcation Analysis and Impulsive Control of Genetic Regulatory Networks with Multi Delays
    Liu, Feng
    Ren, Jie
    Dong, Ting
    Zheng, Shiqi
    JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS, 2019, 23 (04) : 743 - 748
  • [6] Hopf bifurcation analysis of two neurons with three delays
    Huang, Chuangxia
    He, Yigang
    Huang, Lihong
    Yuan Zhaohui
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2007, 8 (03) : 903 - 921
  • [7] Stability and Hopf bifurcation of fractional genetic regulatory networks with diffusion
    Yue, Dandan
    Guan, Zhi-Hong
    Chi, Ming
    Hu, Bin
    Liu, Zhi-Wei
    Chen, Jie
    IFAC PAPERSONLINE, 2017, 50 (01): : 10443 - 10448
  • [8] Multistability and Bifurcation Analysis of Inhibitory Coupled Cyclic Genetic Regulatory Networks With Delays
    Ling, Guang
    Guan, Zhi-Hong
    Hu, Bin
    Lai, Qiang
    Wu, Yonghong
    IEEE TRANSACTIONS ON NANOBIOSCIENCE, 2017, 16 (03) : 216 - 225
  • [9] Stability and bifurcation analysis of new coupled repressilators in genetic regulatory networks with delays
    Ling, Guang
    Guan, Zhi-Hong
    He, Ding-Xin
    Liao, Rui-Quan
    Zhang, Xian-He
    NEURAL NETWORKS, 2014, 60 : 222 - 231
  • [10] Stability and Bifurcation Analysis of Cyclic Genetic Regulatory Networks with Mixed Time Delays
    Ling, Guang
    Guan, Zhi-Hong
    Liao, Rui-Quan
    Cheng, Xin-Ming
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2015, 14 (01): : 202 - 220
12345