Global Exponential Stability Analysis for A Class of Coupled Cyclic Genetic Regulatory Networks with Multiple Time-Varying Delays

Abstract

The coupled repressilators, as a special case of cyclic genetic regulatory networks, can be used to adjust oscillations at the cellular level, and hence it have received extensive attention from many scholars. This paper addresses the problem of global exponential stability analysis for nonnegative equilibrium points of a class of coupled repressilator models with multiple time-varying delays. Sufficient conditions are investigated to guarantee that the considered model has a unique nonnegative equilibrium point which is globally exponentially stable. The obtained criteria are composed of several simple linear inequalities that are only related to the model parameters, so they can be easily verified by using the standard software tools. The results of two illustrative examples present the effectiveness of the proposed approach.