Gomez, Marcella M.Sadeghpour, MehdiBennett, Matthew R.Orosz, GáborMurray, Richard M.2017-05-152017-05-152016Gomez, Marcella M., Sadeghpour, Mehdi, Bennett, Matthew R., et al.. "Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks." <i>SIAM Journal on Applied Dynamical Systems,</i> 15, no. 4 (2016) SIAM: 1844-1873. http://dx.doi.org/10.1137/15M1031965.https://hdl.handle.net/1911/94278The 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.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articlestabilitystochastic delaysystems biologygenetic networkshttp://dx.doi.org/10.1137/15M1031965