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

作者：Liu, Tingting; Zhang, Xian; Gao, Xiangyu^*

来源：Applied Mathematics and Computation, 2016, 274: 628-643.

DOI：10.1016/j.amc.2015.11.040

• GRNs
• Exponential stability
• Dini derivative method
• Semi-discretization technique
• IMEX-theta method
• Linear matrix inequality(LMI) method

Convergent dynamics are investigated in this paper for the genetic regulatory networks (GRNs) with delays in both the continuous-time case and the discrete-time form. First, by utilizing the Lyapunov functional method and some inequality techniques, sufficient criterion is derived to ensure the global exponential stability of the continuous-time GRNs. Second, by using the semi-discretization technique and the IMEX-theta method as sources of reference, two discrete-time analogues of the continuous-time GRN model are formulated respectively. Moreover, it is shown that under the same sufficient conditions derived earlier, these two discrete-time GRN systems are also globally exponentially stable, and the explicit exponential convergent rates are also given. Finally, a numerical example is illustrated to show the validity of the obtained theoretical results, and comparisons of the convergent rates for these two different discrete-time analogues are also demonstrated.

• 出版日期2016-2-1
• 单位黑龙江大学