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Internal signal stochastic resonance of a two-component gene regulatory network under Lévy noise

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Abstract

Noises are ubiquitous in nature and can often induce some curious phenomena. In this paper, we investigate the internal signal stochastic resonance (ISSR) phenomenon of a two-component gene regulatory network under the excitation of Lévy noise. Our results reveal that the Lévy noise can induce the periodic oscillation of the protein concentration when the control parameter is close to its bifurcation points. Furthermore, we consider the noise-induced periodic signal as the periodic excitation and study the ISSR phenomenon under the cooperation of the nonlinear system, noise-induced periodic signal and random noise. And we found that there may be a connection between the ISSR phenomenon and the bifurcation mechanism. Besides, we also investigate the effects of different noise parameters on the ISSR phenomenon. The simulation results indicate that there is an optimal interval of the stability index \(\alpha \) which can induce the ISSR phenomenon, and the skewness parameter \(\beta \) has a negative correlation with the ISSR phenomenon. Our results may provide a pathway to uncover the positive functional mechanism of noises in complex gene regulatory networks.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (11772291). The authors would like to thank the reviewers for their comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China

    Q. H. Zhu

  2. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, 450046, Zhengzhou, China

    J. W. Shen

  3. School of Mathematics and Statistics, Xuchang University, 461000, Xuchang, China

    J. W. Shen

  4. School of Mechanical and Mechatronic Engineering, FEIT, University of Technology Sydney, PO Box 123, Broadway, NSW, 2007, Australia

    J. C. Ji

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  1. Q. H. Zhu
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  3. J. C. Ji
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Correspondence to J. W. Shen.

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Zhu, Q.H., Shen, J.W. & Ji, J.C. Internal signal stochastic resonance of a two-component gene regulatory network under Lévy noise. Nonlinear Dyn 100, 863–876 (2020). https://doi.org/10.1007/s11071-020-05489-7

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  • DOI: https://doi.org/10.1007/s11071-020-05489-7

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