Stability and bifurcation of genetic regulatory networks with delays

被引：33

作者：

Wang, Kai ^{[1
,2
]}

Wang, Lei ^{[2
]}

Teng, Zhidong ^{[1
]}

Jiang, Haijun ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Xinjiang Med Univ, Dept Med Engn & Technol, Urumqi 830059, Peoples R China

来源：

NEUROCOMPUTING | 2010年 / 73卷 / 16-18期

关键词：

Hopf bifurcation; Periodic solution; Genetic regulatory networks; Time delay; ROBUST STABILITY; EXPONENTIAL STABILITY; HOPF-BIFURCATION; SIMULATION; SYSTEM; NOISE;

D O I：

10.1016/j.neucom.2010.08.009

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

A four-dimension genetic regulatory network model with double genes and four delays is considered. The existence of Hopf bifurcation is first considered and then explicit formulas are derived by using the normal form method and center manifold theory to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions. Finally, numerical simulations are carried out to support the theoretical analysis of the research. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：2882 / 2892

页数：11

共 24 条

[1] Gene network shaping of inherent noise spectra [J].

Austin, DW ;

Allen, MS ;

McCollum, JM ;

Dar, RD ;

Wilgus, JR ;

Sayler, GS ;

Samatova, NF ;

Cox, CD ;

Simpson, ML .

NATURE, 2006, 439 (7076) :608-611

[2] Engineering stability in gene networks by autoregulation [J].

Becskei, A ;

Serrano, L .

NATURE, 2000, 405 (6786) :590-593

[3] Stability of genetic regulatory networks with time delay [J].

Chen, LN ;

Aihara, K .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2002, 49 (05) :602-608

[4] Modeling and simulation of genetic regulatory systems: A literature review [J].

De Jong, H .

JOURNAL OF COMPUTATIONAL BIOLOGY, 2002, 9 (01) :67-103

[5] A synthetic oscillatory network of transcriptional regulators [J].

Elowitz, MB ;

Leibler, S .

NATURE, 2000, 403 (6767) :335-338

[6] Construction of a genetic toggle switch in Escherichia coli [J].

Gardner, TS ;

Cantor, CR ;

Collins, JJ .

NATURE, 2000, 403 (6767) :339-342

[7]

Hale J.K., 1977, THEORY FUNCTIONAL DI

[8]

Hassard B.D., 1981, Theory and Applications of Hopf Bifurcation

[9] Robust stability of genetic regulatory networks with distributed delay [J].

He, Wangli ;

Cao, Jinde .

COGNITIVE NEURODYNAMICS, 2008, 2 (04) :355-361

[10] Modeling genetic switches with positive feedback loops [J].

Kobayashi, T ;

Chen, LN ;

Aihara, K .

JOURNAL OF THEORETICAL BIOLOGY, 2003, 221 (03) :379-399

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