Global uniform asymptotical stability for fractional-order gene regulatory networks with time-varying delays and structured uncertainties

Advances in Difference Equations

Tiejun Zhou¹  Zhaohua Wu²  Zhiming Wang³ 

[1] College of Information and Intelligence Science, Hunan Agricultural University, 410128, Changsha, P.R. China;School of Mathematics and Statistics, Huaiyin Normal University, 223300, Huaian, P.R. China;School of Mathematics and Statistics, Huaiyin Normal University, 223300, Huaian, P.R. China;School of Computer Science and Technology, Huaiyin Normal University, 223300, Huaian, P.R. China;

关键词: Fractional-order;    Gene regulatory networks;    Time-varying delays;    Uniform asymptotical stability;    34D23;    34A08;    05C82;   

DOI  :  10.1186/s13662-021-03243-w

来源: Springer

【 摘 要 】

In this paper, we investigate a class of fractional-order gene regulatory networks with time-varying delays and structured uncertainties (UDFGRNs). First, we deduce the existence and uniqueness of the equilibrium for the UDFGRNs by using the contraction mapping principle. Next, we derive a novel global uniform asymptotic stability criterion of the UDFGRNs by using a Lyapunov function and the Razumikhin technique, and the conditions relating to the criterion depend on the fractional order of the UDFGRNs. Finally, we provide two numerical simulation examples to demonstrate the correctness and usefulness of the novel stability conditions. One of the most interesting findings is that the structured uncertainties indeed have an impact on the stability of the system.

【 授权许可】

CC BY