Abstract
This work studies global exponential stability analysis for a class of nonlinear genetic regulatory networks (GRNs) with two-coupled-hub structure and time-varying delays. It is important to study the influence of hub genes in GRNs problem, due to there is the complexity arising from the interactions among hub gene nodes. In this article, the existence of GRN’s nonnegative equilibriums is presented and a sufficient condition such that all nonnegative equilibriums are positive can be further proved. In addition, novel global exponential stability (GES) criteria of coupled nonlinear GRN is established based on a Metzler matrix method. Furthermore, under the proposed delay-dependent and -independent GES sufficient conditions, it proves the considered GRNs has a unique non-negative GES equilibrium point. Compared with the existing GES criteria, it is worth stressing that the proposed GES conditions are easily verified by computing relative matrices eigenvalues and induced norms. Finally, the validity of the theoretical results is verified by three simulation examples.
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