Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

Advances in Difference Equations

Ming Ye¹  Boqiang Cao²  Qimin Zhang² 

[1] Department of Scientific Computing, Florida State University, Tallahassee, USA;School of Mathematics and Statistics, Ningxia University, Yinchuan, P.R. China

关键词: genetic regulatory networks;    exponential stability;    impulsive;    reaction-diffusion;    factional Brownian motion;   

DOI  :  10.1186/s13662-016-1033-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. An example is presented to illustrate our results of the mean-square exponential stability analysis.

【 授权许可】

CC BY