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SCIENCE CHINA Information Sciences, Volume 59, Issue 1: 012202(2016) https://doi.org/10.1007/s11432-015-5357-z

Sufficient and necessary conditions for global stability of genetic regulator networks with time delays

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  • ReceivedMar 16, 2015
  • AcceptedMay 4, 2015
  • PublishedDec 21, 2015

Abstract

This paper is concerned with the global stability of the nonlinear model for genetic regulator networks (GRNs) with time delays. Four new sufficient and necessary conditions for global asymptotic stability and global exponential stability of the equilibrium point of GRNs are derived. Specifically, using comparing theorem and Dini derivation method, three weak sufficient conditions for global stability of GRNs with constant time delays are proposed. Finally, a general GRN model is used to illustrate the effectiveness of the proposed theoretical results. Compared with the previous results, some sufficient and necessary conditions for Lyapunov stability of GRNs are proposed, which are not seen before.


Funded by

hubei Natural Science Foundation(2012FFB4102)

national Natural Science Foundation of China(61340042)

hubei Science and Technology Support Program(2015BAA001)

Hubei SMEs Innovation Fund Project(2015DAL069)

hubei Natural Science Foundation(2013CFC011)


Acknowledgment

Acknowledgments

This work was supported by national Natural Science Foundation of China (Grant No. 61340042), hubei Natural Science Foundation (Grant Nos. 2013CFC011, 2012FFB4102), hubei Science and Technology Support Program (Grant No. 2015BAA001), and Hubei SMEs Innovation Fund Project (Grant No. 2015DAL069).


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