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Stability of gene regulatory networks with Lévy noise

Abstract

The stability of gene regulatory networks has attracted substantial research efforts in the field of systematic biology. Actual gene regulatory networks are always subject to noise interference and disruption to the organism either internally or externally. Specifically, the special case of instantaneous mutation may exist in gene regulatory networks at the mRNA or protein level. Compared with other existing models, a Lévy noise-driven gene regulatory network model has been proved to be more realistic, since it is a powerful tool to describe the above special case. On the basis of previous studies, we developed a theoretical proof of the Lévy noise- driven gene regulatory network, and carried out a large number of numerical simulations for validation. Based on adequate analysis of the simulation examples, the sufficient conditions were investigated and are presented herein to obtain the global asymptotic stability of gene regulatory networks with time-varying delays and Lévy noise.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61573193) and Joint Key Grant of National Natural Science Foundation of China and Zhejiang Province (Grant No. U1509217).

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Correspondence to Yangyang Gong.

Additional information

Conflict of interest The authors declare that they have no conflict of interest.

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Luo, Q., Gong, Y. & Jia, C. Stability of gene regulatory networks with Lévy noise. Sci. China Inf. Sci. 60, 072204 (2017). https://doi.org/10.1007/s11432-016-0526-8

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Keywords

  • Lévy noise
  • gene regulatory networks
  • time-varying delays
  • stability analysis
  • instantaneous mutation