Exponential stability of genetic regulatory networks with random delays
Exponential stability of genetic regulatory networks with random delays
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DOI：
10.1016/j.neucom.2009.10.006
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发表时间：
2010
期刊：
影响因子：
6
通讯作者：
X. Lou;Q. Ye;B. Cui
中科院分区：
文献类型：
--
作者：
X. Lou;Q. Ye;B. Cui
本文研究了遗传调控网络（GRNs）均方意义下的全局指数稳定性，其动机是考虑到不同基因的转录和翻译具有不同的时间延迟，并且在某些情况下，每个多聚体被分配到一个随机选择的基因启动子位点作为激活剂或抑制剂.这里报告所获得的结果的一个重要特征是，时变时滞被假定为随机的，其概率分布是已知的先验。利用时滞的概率分布信息，给出了具有SUM调控逻辑的不确定时滞遗传网络的稳定性判据，其中每个转录因子都参与调控一个基因.该方法同时考虑了时滞的变化范围和分布概率的影响。结果的另一个特点是，一个新的李雅普诺夫函数依赖于辅助延迟参数，这使得结果是潜在的保守性较低，并允许时变延迟是不可微的。理论研究结果进行了说明，并验证了两个例子。
This paper on global exponential stability in the mean square sense of genetic regulatory networks (GRNs) is motivated by a practical consideration that different genes have different time delays for transcription and translation, and in some cases, each multimer is assigned to a randomly chosen gene promoter site as an activator or inhibitor. One important feature of the obtained results reported here is that the time-varying delays are assumed to be random and their probability distributions are known a priori. By employing the information of the probability distributions of the time delays, we present some stability criteria for the uncertain delayed genetic networks with SUM regulatory logic where each transcription factor acts additively to regulate a gene. The effects of both variation range and distribution probability of the time delays are taken into account in the proposed approach. Another feature of the results is that a novel Lyapunov functional dependence on auxiliary delay parameters is exploited, which renders the results to be potentially less conservative and allows the time-varying delays to be not differentiable. The theoretical findings are illustrated and verified with two examples.