 Stability analysis for continuous-time and discrete-time genetic regulatory networks with delaysTingting Liu, Xian Zhang and Xiangyu Gao Applied Mathematics and Computation, 2016, vol. 274, issue C, 628-643 Abstract: This paper investigates the global exponential stability problem for the genetic regulatory networks (GRNs) with delays in both the continuous-time case and the discrete-time case. First, Dini derivative method is applied for a new Lyapunov functional to obtain a sufficient condition of the global exponential stability for a class of the continuous-time GRNs, which is given in the form of several elementary inequalities. This sufficient condition is simple to be easily implemented on the computer. Second, by using the semi-discretization technique and the IMEX-θ method, two discrete-time GRN systems have been derived, which can preserve the dynamical characteristics of the continuous-time systems. Furthermore, it is shown that under the same sufficient conditions obtained earlier, these two discrete-time GRN systems are globally exponentially stable. Finally, a pair of examples are given to show the validity of the obtained stability analysis results. Keywords: GRNs; Exponential stability; Dini derivative method; Semi-discretization technique; IMEX-θ method; Linear matrix inequality(LMI) method (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:274:y:2016:i:c:p:628-643 DOI: 10.1016/j.amc.2015.11.040 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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