Mean-Square Exponential Input-to-State Stability of Stochastic Gene Regulatory Networks with Multiple Time Delays

Abstract

This paper is concerned with the input-to-state stability of stochastic gene regulatory networks with multiple time delays. It is well acknowledged that stochastic systems can accurately describe some complex systems with random disturbances. So it is significant that stochastic systems are applied to model gene regulatory networks because of the complex relationship between genes and proteins from a micro perspective. Considering the differences between stochastic differential equations and ordinary differential equations, we introduce the new stability criterion which is different from the general stability criteria. Making use of Lyapunov functionals, It$$\hat{o}$$ formula and Dynkin formula, we present sufficient conditions to guarantee that the proposed system is mean-square exponentially input-to-state stable. Moreover, numerical examples are given to illustrate validity and feasibility of the obtained results.