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Published October 13, 2016 | Version Supplemental Material + Accepted Version + Published
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Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks

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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 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.

Additional Information

© 2016 Society for Industrial and Applied Mathematics. Received by the editors July 22, 2015; accepted for publication (in revised form) by J. Sieber July 27, 2016; published electronically October 13, 2016. The research of the first author was supported by the TerraSwarm Research Center, one of six centers supported by the STARnet phase of the Focus Center Research Program (FCRP), a Semiconductor Research Corporation program sponsored by MARCO and DARPA. The research of the second and fourth authors was supported by the National Science Foundation (award 1300319). The research of the third author was supported by the NIH, through the joint NSF/NIGMS Mathematical Biology Program under grant R01GM104974, and by the Robert A. Welch Foundation under grant C-1729. The authors would like to thank Mark J. Balas for helpful discussions.

Attached Files

Published - 15m1031965.pdf

Accepted Version - nihms874233.pdf

Supplemental Material - M103196_01.zip

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Additional details

Identifiers

PMCID
PMC5603244
Eprint ID
73975
Resolver ID
CaltechAUTHORS:20170202-073327562

Funding

Defense Advanced Research Projects Agency (DARPA)
NSF
CMMI-1300319
NIH
R01GM104974
Robert A. Welch Foundation
C-1729
Microelectronics Advanced Research Corporation (MARCO)
TerraSwarm

Dates

Created
2017-02-02
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Updated
2023-07-05
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