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.

中文翻译：

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具有随机时滞的系统的稳定性及其在遗传调控网络中的应用。

本文研究了具有随机变化时滞的系统的动力学特性。结果表明，平均动力学可以用来推导随机系统平衡稳定性的必要条件。此外，第二矩动力学可用于得出几乎可以肯定的平衡稳定性的条件。使用通过半离散获得的稳定性图表总结了结果。理论方法被应用于简单的基因调控网络，其中证明了延迟中的随机性可以提高稳定蛋白质生产的稳定性。