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

作者信息

Gomez Marcella M, Sadeghpour Mehdi, Bennett Matthew R, Orosz Gábor, Murray Richard M

机构信息

Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA.

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.

出版信息

SIAM J Appl Dyn Syst. 2016;15(4):1844-1873. doi: 10.1137/15M1031965. Epub 2016 Oct 13.

DOI:10.1137/15M1031965
PMID:28936130
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5603244/
Abstract

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 semi-discretization. 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.

摘要

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