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Local Bifurcation Analysis of a Fractional-Order Dynamic Model of Genetic Regulatory Networks with Delays

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Intelligent Computing, Networked Control, and Their Engineering Applications (ICSEE 2017, LSMS 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 762))

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Abstract

This paper proposes a mathematical model of gene networks, which includes the fractional derivative and delays. We obtain the conditions of the stability and Hopf bifurcation, and find that a Hopf bifurcation occurs when the sum of delays crosses the critical value, which can be calculated exactly. The fractional order can be used to effectively control the dynamics of such fractional-order model, and the stability domain can be changed by manipulated the order. Finally, a numerical example is presented to demonstrate the theoretical analysis.

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Acknowledgments

This paper is supported by National Natural Science Foundation of China (No. 61573194), Science Foundation of Nanjing University of Posts and Telecommunications (NY213095).

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Authors and Affiliations

  1. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Qingshan Sun, Min Xiao & Binbin Tao

  2. College of Information Engineering, Nanjing Xiaozhuang University, Nanjing, 210017, China

    Lingzhi Zhao

Authors
  1. Qingshan Sun
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  2. Min Xiao
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  3. Lingzhi Zhao
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  4. Binbin Tao
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Corresponding author

Correspondence to Min Xiao .

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Editors and Affiliations

  1. Nanjing University of Posts and Telecommunications, Nanjing, China

    Dong Yue

  2. Shanghai University , Shanghai, China

    Chen Peng

  3. Shanghai University , Shanghai, China

    Dajun Du

  4. Nanjing University of Posts and Telecommunications, Nanjing, China

    Tengfei Zhang

  5. Shanghai University , Shanghai, China

    Min Zheng

  6. Swinburne University of Technology, Melbourne, Victoria, Australia

    Qinglong Han

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© 2017 Springer Nature Singapore Pte Ltd.

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Sun, Q., Xiao, M., Zhao, L., Tao, B. (2017). Local Bifurcation Analysis of a Fractional-Order Dynamic Model of Genetic Regulatory Networks with Delays. In: Yue, D., Peng, C., Du, D., Zhang, T., Zheng, M., Han, Q. (eds) Intelligent Computing, Networked Control, and Their Engineering Applications. ICSEE LSMS 2017 2017. Communications in Computer and Information Science, vol 762. Springer, Singapore. https://doi.org/10.1007/978-981-10-6373-2_51

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  • DOI: https://doi.org/10.1007/978-981-10-6373-2_51

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6372-5

  • Online ISBN: 978-981-10-6373-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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