Stability and Bifurcation Analysis of Cyclic Genetic Regulatory Networks with Mixed Time Delays

被引：38
作者：
Ling, Guang [1 ,2 ]
Guan, Zhi-Hong [1 ,2 ]
Liao, Rui-Quan [3 ]
Cheng, Xin-Ming [4 ]
机构：
[1] Huazhong Univ Sci & Technol, Coll Automat, Wuhan 430074, Peoples R China
[2] Huazhong Univ Sci & Technol, Key Lab Image Informat Proc & Intelligent Control, Minist Educ, Wuhan 430074, Peoples R China
[3] Yangtze Univ, Petr Engn Coll, Jinzhou 434023, Peoples R China
[4] Cent S Univ, Sch Informat Sci & Engn, Changsha 430083, Hunan, Peoples R China
来源：
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2015年 / 14卷 / 01期
基金：
中国国家自然科学基金;
关键词：
cyclic genetic regulatory networks; stability criteria; periodic oscillations; Hopf bifurcation; mixed time delays; HOPF-BIFURCATION; DISTRIBUTED DELAY; ROBUST STABILITY; FEEDBACK-SYSTEMS; OSCILLATIONS; REPRESSILATORS; EXPRESSION; EXISTENCE; MODEL;
D O I：
10.1137/140954131
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper analyzes the stability and bifurcation criteria of cyclic genetic regulatory networks with mixed time delays (discrete and Gamma-type distributed delays). It is of more realistic biological background to use Gamma-type distributed delay kernels to describe the delays in the process between genes. The key aim of our research is to reveal more about the dynamic functions played by biochemical parameters and different mechanisms of discrete and distributed time delays. The existence of positive equilibria in this kind of genetic network is verified. With the mathematical tools of subharmonic function and complex theory, exact conditions of biochemical parameters for stability and bifurcations in cyclic genetic regulatory networks with both positive and negative gains are deduced, respectively. Finally, several simulation examples are adopted to deepen our analysis.
引用
收藏
页码：202 / 220
页数：19
相关论文
共 27 条
  • [1] Alon U., 2006, INTRO SYSTEMS BIOL D, DOI [10.1201/9781420011432, DOI 10.1201/9781420011432]
  • [2] Subharmonic Functions and Performance Bounds on Linear Time-Invariant Feedback Systems
    Boyd, Stephen
    Desoer, C. A.
    [J]. IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 1985, 2 (02) : 153 - 170
  • [3] Stability of genetic regulatory networks with time delay
    Chen, LN
    Aihara, K
    [J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2002, 49 (05) : 602 - 608
  • [4] Local and Global Stability of Equilibria for a Class of Chemical Reaction Networks
    Donnell, Pete
    Banaji, Murad
    [J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2013, 12 (02): : 899 - 920
  • [5] Repressilators and promotilators: Loop dynamics in synthetic gene networks
    El Samad, H
    Del Vecchio, D
    Khammash, A
    [J]. ACC: PROCEEDINGS OF THE 2005 AMERICAN CONTROL CONFERENCE, VOLS 1-7, 2005, : 4405 - 4410
  • [6] A synthetic oscillatory network of transcriptional regulators
    Elowitz, MB
    Leibler, S
    [J]. NATURE, 2000, 403 (6767) : 335 - 338
  • [7] Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations
    Gupta, Chinmaya
    Lopez, Jose Manuel
    Azencott, Robert
    Bennett, Matthew R.
    Josic, Kresimir
    Ott, William
    [J]. JOURNAL OF CHEMICAL PHYSICS, 2014, 140 (20)
  • [8] Robust stability of genetic regulatory networks with distributed delay
    He, Wangli
    Cao, Jinde
    [J]. COGNITIVE NEURODYNAMICS, 2008, 2 (04) : 355 - 361
  • [9] Biochemical oscillations in delayed negative cyclic feedback: Existence and profiles
    Hori, Yutaka
    Takada, Masaaki
    Hara, Shinji
    [J]. AUTOMATICA, 2013, 49 (09) : 2581 - 2590
  • [10] Existence criteria of periodic oscillations in cyclic gene regulatory networks
    Hori, Yutaka
    Kim, Tae-Hyoung
    Hara, Shinji
    [J]. AUTOMATICA, 2011, 47 (06) : 1203 - 1209
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