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Stability of Genetic Regulatory Networks with Multiple Delays via a New Functional

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Advances in Neural Networks - ISNN 2010 (ISNN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6063))

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Abstract

This paper studies the stability problem of a class of genetic regulatory networks (GRN) with multiple delays. By using a novel Lyapunov-Krasovskii (L-K) functional based on line integral, the delay-dependent asymptotical stability criterion is first proposed for GRN with multiple delays. The obtained stability result is easy to be checked by linear matrix inequality (LMI) and improve upon the existing ones. Then, a numerical example is given to verify the effectiveness of the proposed criterion.

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References

  1. Yu, W., Lü, J., Chen, G., Duan, Z., Zhou, Q.: Estimating Uncertain Delayed Genetic Regulatory Networks: An Adaptive Filtering Approach. IEEE Trans. Autom. Contr. 54, 892–897 (2009)

    Article  Google Scholar 

  2. Becskel, A., Serrano, L.: Engineering Stability in Gene Networks by Autoregulation. Nature 405, 590–593 (2000)

    Article  Google Scholar 

  3. Chen, L., Aihara, K.: Stability of Genetic Regulatory Networks with Time Delay. IEEE Trans. Circu. Syst. I: Fundam. Theory Appl. 49, 602–608 (2002)

    Article  MathSciNet  Google Scholar 

  4. Ren, F., Cao, J.: Asymptotic and Robust Stability of Genetic Regulatory Networks with Time-Varying Delays. Neurocomputing 71, 834–842 (2008)

    Article  Google Scholar 

  5. Cao, J., Ren, F.: Exponential Stability of Discrete-Time Genetic Regulatory Networks with Delays. IEEE Trans. Neural Netw. 19, 520–523 (2008)

    Article  Google Scholar 

  6. Wang, Z., Gao, H., Cao, J., Liu, X.: On Delayed Genetic Regulatory Networks With Polytopic Uncertainties: Robust Stability Analysis. IEEE Trans. Nanobioscience 7, 154–163 (2008)

    Article  Google Scholar 

  7. Mahaffy, J.M., Pao, C.V.: Models of Genetic Control by Repression with Time Delays and Spatial Effects. J. Math. Biol. 20, 39–57 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  8. Monk, N.A.M.: Oscillatory Expression of Hes1, p53, and NF-κ B Driven by Transcriptional Time Delays. Current Biol. 13, 1409–1413 (2003)

    Article  Google Scholar 

  9. Yuh, C.-H., Bolouri, H., Davidson, E.H.: Genomic Cis-Regulatory Logic: Experimental and Computational Analysis of Asea Urchin Gene. Science 279, 1896–1902 (1998)

    Article  Google Scholar 

  10. Kalir, S., Mangan, S., Alon, U.: A Coherent Feed-Forward Loop with A SUM Input Function Prolongs Flagella Expression in Escherichia Coli. Molecular Syst. Biol. (2005), doi:10.1038/msb4100010

    Google Scholar 

  11. Hubbard, J., Hubbard, B.B.: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, 3rd edn., Matrix, New York, USA (2007)

    Google Scholar 

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Author information

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, P.R. China

    Zhenwei Liu & Huaguang Zhang

Authors
  1. Zhenwei Liu
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  2. Huaguang Zhang
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, 200240, Shanghai, China

    Liqing Zhang

  2. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 800, Dongchuan Road, 200240, Shanghai, China

    Bao-Liang Lu

  3. Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water bay, Kowloon, Hong Kong, China

    James Kwok

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Liu, Z., Zhang, H. (2010). Stability of Genetic Regulatory Networks with Multiple Delays via a New Functional. In: Zhang, L., Lu, BL., Kwok, J. (eds) Advances in Neural Networks - ISNN 2010. ISNN 2010. Lecture Notes in Computer Science, vol 6063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13278-0_65

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  • DOI: https://doi.org/10.1007/978-3-642-13278-0_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13277-3

  • Online ISBN: 978-3-642-13278-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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