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

页码：202 / 220

页数：19

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