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Stability analysis for continuous-time and discrete-time genetic regulatory networks with delays

Author

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  • Liu, Tingting
  • Zhang, Xian
  • Gao, Xiangyu

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.

Suggested Citation

  • Liu, Tingting & Zhang, Xian & Gao, Xiangyu, 2016. "Stability analysis for continuous-time and discrete-time genetic regulatory networks with delays," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 628-643.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:628-643
    DOI: 10.1016/j.amc.2015.11.040
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    Cited by:

    1. Jiao, Ticao & Park, Ju H. & Zong, Guangdeng & Liu, Jian & Chen, Yu, 2019. "Stochastic stability analysis of switched genetic regulatory networks without stable subsystems," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 261-277.

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