Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks

被引：12

作者：

Gomez, Marcella M. ^{[1
]}

Sadeghpour, Mehdi ^{[2
]}

Bennett, Matthew R. ^{[3
,4
]}

Orosz, Gabor ^{[2
]}

Murray, Richard M. ^{[5
]}

机构：

[1] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA

[2] Univ Michigan, Dept Mech Engn, Ann Arbor, MI 48109 USA

[3] Rice Univ, Dept Comp & Math Sci, Houston, TX 77005 USA

[4] Rice Univ, Dept Bioengn, Houston, TX 77005 USA

[5] CALTECH, Control & Dynam Syst, Pasadena, CA 91125 USA

来源：

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2016年 / 15卷 / 04期

基金：

美国国家科学基金会;

关键词：

stability; stochastic delay; systems biology; genetic networks; DIFFERENTIAL-EQUATIONS; TIME-DELAY; EXPONENTIAL STABILITY; SEMI-DISCRETIZATION; DYNAMICAL-SYSTEMS; STABILIZATION; NOISE; OSCILLATOR; BIFURCATION; ROBUST;

D O I：

10.1137/15M1031965

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The dynamics of systems with stochastically varying time delays are investigated in this paper. It is shown that the mean dynamics can be used to derive necessary conditions for the stability of equilibria of the stochastic system. Moreover, the second moment dynamics can be used to derive sufficient conditions for almost sure stability of equilibria. The results are summarized using stability charts that are obtained via semidiscretization. The theoretical methods are applied to simple gene regulatory networks where it is demonstrated that stochasticity in the delay can improve the stability of steady protein production.

引用

页码：1844 / 1873

页数：30

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