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Switch dynamics in a genetic toggle network driven by Lévy noise

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Abstract

The noise may drive the genetic toggle network switch from one stable state to another. To describe transcriptional bursting in synthesis process of biochemical systems, the Lévy noise is introduced to genetic toggle network with kinetic parameters and the dynamical transition is investigated via two deterministic quantities, the first escape probability and mean first exit time. Firstly, the analytical expressions of that two deterministic quantities in irregular domain are derived from the governing differential-integral equation. Then, the numerical schemes of the two indexes are developed by the finite difference method, and the validity of the proposed method is verified by the Monte Carlo simulations. Analyzing the Lévy noise on the switch mechine, we found that a decreasing stability index or an increasing noise intensity can reduce the probability of the first switching from the (low, high) state to the (high, low) state. Furthermore, higher noise intensity and stability index shorten the residence time of the (low, high) state.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors thank the reviewers and editors for their careful reading and suggestions. This work is supported by the National Natural Science Foundation of China (Grant Nos. 12072261 and 11872305) and by Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant No. CX2022069).

Funding

Funding was provided by the National Natural Science Foundation of China (Grant Nos. 12072261,11872305), and by Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant No. CX2022069).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Yi Song, Wei Xu, Wei Wei & Lizhi Niu

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  1. Yi Song
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Contributions

All authors contributed to the study conception. YS and WX designed and performed the research; YS and WW were responsible for programming; and YS and LN wrote the article.

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Correspondence to Wei Xu.

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Song, Y., Xu, W., Wei, W. et al. Switch dynamics in a genetic toggle network driven by Lévy noise. Nonlinear Dyn 110, 3779–3790 (2022). https://doi.org/10.1007/s11071-022-07781-0

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