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

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. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.
Authors:
 [1] ;  [1] ;  [2]
  1. Ningxia Univ., Yinchuan (China). School of Mathematics and Statistics
  2. 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 1687-1847
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; reaction-diffusion; factional Brownian motion
OSTI Identifier:
1426173

Cao, Boqiang, Zhang, Qimin, and Ye, Ming. Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion. United States: N. p., Web. doi:10.1186/s13662-016-1033-x.
Cao, Boqiang, Zhang, Qimin, & Ye, Ming. Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion. United States. doi:10.1186/s13662-016-1033-x.
Cao, Boqiang, Zhang, Qimin, and Ye, Ming. 2016. "Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion". United States. doi:10.1186/s13662-016-1033-x. https://www.osti.gov/servlets/purl/1426173.
@article{osti_1426173,
title = {Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion},
author = {Cao, Boqiang and Zhang, Qimin and Ye, Ming},
abstractNote = {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. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.},
doi = {10.1186/s13662-016-1033-x},
journal = {Advances in Difference Equations},
number = 1,
volume = 2016,
place = {United States},
year = {2016},
month = {11}
}