Exponential stability of impulsive stochastic genetic regulatory networks with timevarying delays and reactiondiffusion
We present a meansquare exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with timevarying delays and reactiondiffusion 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 meansquare sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the meansquare exponential stability analysis.
 Authors:

^{[1]};
^{[1]};
^{[2]}
 Ningxia Univ., Yinchuan (China). School of Mathematics and Statistics
 Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing
 Publication Date:
 Grant/Contract Number:
 SC0008272; 1552329
 Type:
 Accepted Manuscript
 Journal Name:
 Advances in Difference Equations
 Additional Journal Information:
 Journal Volume: 2016; Journal Issue: 1; Journal ID: ISSN 16871847
 Publisher:
 Springer  Hindawi
 Research Org:
 Florida State Univ., Tallahassee, FL (United States)
 Sponsoring Org:
 USDOE; National Natural Science Foundation of China (NNSFC); National Science Foundation (NSF)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 59 BASIC BIOLOGICAL SCIENCES; genetic regulatory networks; exponential stability; impulsive; reactiondiffusion; factional Brownian motion
 OSTI Identifier:
 1426173
Cao, Boqiang, Zhang, Qimin, and Ye, Ming. Exponential stability of impulsive stochastic genetic regulatory networks with timevarying delays and reactiondiffusion. United States: N. p.,
Web. doi:10.1186/s136620161033x.
Cao, Boqiang, Zhang, Qimin, & Ye, Ming. Exponential stability of impulsive stochastic genetic regulatory networks with timevarying delays and reactiondiffusion. United States. doi:10.1186/s136620161033x.
Cao, Boqiang, Zhang, Qimin, and Ye, Ming. 2016.
"Exponential stability of impulsive stochastic genetic regulatory networks with timevarying delays and reactiondiffusion". United States.
doi:10.1186/s136620161033x. https://www.osti.gov/servlets/purl/1426173.
@article{osti_1426173,
title = {Exponential stability of impulsive stochastic genetic regulatory networks with timevarying delays and reactiondiffusion},
author = {Cao, Boqiang and Zhang, Qimin and Ye, Ming},
abstractNote = {We present a meansquare exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with timevarying delays and reactiondiffusion 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 meansquare sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the meansquare exponential stability analysis.},
doi = {10.1186/s136620161033x},
journal = {Advances in Difference Equations},
number = 1,
volume = 2016,
place = {United States},
year = {2016},
month = {11}
}