Robust stability of stochastic delayed genetic regulatory networks

Gene regulation is an intrinsically noisy process, which is subject to intracellular and extracellular noise perturbations and environment fluctuations. In this paper, we consider the robust stability analysis problem of genetic regulatory networks with time-varying delays and stochastic perturbation. Different from other papers, the genetic regulate system considers not only stochastic perturbation but also parameter disturbances, it is in close proximity to the real gene regulation process than determinate model. Based on the Lyapunov functional theory, sufficient conditions are given to ensure the stability of the genetic regulatory networks. All the stability conditions are given in terms of LMIs which are easy to be verified. Illustrative examples are presented to show the effectiveness of the obtained results.

[1]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[2]  E. Davidson,et al.  Genomic cis-regulatory logic: experimental and computational analysis of a sea urchin gene. , 1998, Science.

[3]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[4]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[5]  L. Serrano,et al.  Engineering stability in gene networks by autoregulation , 2000, Nature.

[6]  J. Hasty,et al.  Noise-based switches and amplifiers for gene expression. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[7]  D. A. Baxter,et al.  Mathematical Modeling of Gene Networks , 2000, Neuron.

[8]  Guanrong Chen,et al.  Novel robust stability criteria for interval-delayed Hopfield neural networks , 2001 .

[9]  Farren J. Isaacs,et al.  Computational studies of gene regulatory networks: in numero molecular biology , 2001, Nature Reviews Genetics.

[10]  Delay dependent stability for uncertain time-delay systems , 2001 .

[11]  E. Davidson,et al.  Modeling transcriptional regulatory networks. , 2002, BioEssays : news and reviews in molecular, cellular and developmental biology.

[12]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[13]  K. Aihara,et al.  Stability of genetic regulatory networks with time delay , 2002 .

[14]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

[15]  Kazuyuki Aihara,et al.  Modeling genetic switches with positive feedback loops. , 2003, Journal of theoretical biology.

[16]  Ruiqi Wang,et al.  Modelling periodic oscillation of biological systems with multiple timescale networks. , 2004, Systems biology.

[17]  Kazuyuki Aihara,et al.  Dynamics of gene regulatory networks with cell division cycle. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Kevin Burrage,et al.  Stochastic approaches for modelling in vivo reactions , 2004, Comput. Biol. Chem..

[19]  Robust stability for stochastic interval delayed Hopfield neural networks , 2004 .

[20]  Luonan Chen,et al.  Modelling periodic oscillation in gene regulatory networks by cyclic feedback systems , 2005, Bulletin of mathematical biology.

[21]  Zidong Wang,et al.  Robust stability for stochastic Hopfield neural networks with time delays , 2006 .

[22]  K. Aihara,et al.  Synchronization of coupled nonidentical genetic oscillators , 2006, Physical biology.

[23]  Kazuyuki Aihara,et al.  Stability of Genetic Networks With SUM Regulatory Logic: Lur'e System and LMI Approach , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  P. Shi,et al.  Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays , 2007 .

[25]  Zidong Wang,et al.  Exponential stability of uncertain stochastic neural networks with mixed time-delays , 2007 .

[26]  G. Feng,et al.  Delay-dependent stability for uncertain stochastic neural networks with time-varying delay , 2007 .

[27]  Jinde Cao,et al.  Robust stability of genetic regulatory networks with distributed delay , 2008, Cognitive Neurodynamics.

[28]  Jinde Cao,et al.  Asymptotic and robust stability of genetic regulatory networks with time-varying delays , 2008, Neurocomputing.

[29]  Lubica Benuskova,et al.  Modeling brain dynamics using computational neurogenetic approach , 2008, Cognitive Neurodynamics.

[30]  Jinde Cao,et al.  Exponential Stability of Discrete-Time Genetic Regulatory Networks With Delays , 2008, IEEE Transactions on Neural Networks.