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

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Abstract

In this paper, we propose a delayed fractional-order gene regulatory network model. Firstly, the sum of delays is chosen as the bifurcation parameter, and the conditions of the existence for Hopf bifurcations are achieved through analyzing its characteristic equation. Secondly, it is shown that the fractional order can be effectively manipulated to control the dynamics of such network, and the stability domain can be changed with different fractional orders. The fractional-order genetic network can generate a Hopf bifurcation (oscillation appears) as the sum of delays passes through some critical values. Therefore, we can achieve some desirable dynamical behaviors by choosing the appropriate fractional order. Finally, numerical simulations are carried out to illustrate the validity of our theoretical analysis.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (No. 61573194), Six Talent Peaks High Level Project of Jiangsu Province (2014-ZNDW-004) and 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

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  1. Qingshan Sun
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  2. Min Xiao
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  3. Binbin Tao
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Corresponding author

Correspondence to Min Xiao.

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Sun, Q., Xiao, M. & Tao, B. Local Bifurcation Analysis of a Fractional-Order Dynamic Model of Genetic Regulatory Networks with Delays. Neural Process Lett 47, 1285–1296 (2018). https://doi.org/10.1007/s11063-017-9690-7

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  • DOI: https://doi.org/10.1007/s11063-017-9690-7

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