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Most probable dynamics of a genetic regulatory network under stable Lévy noise

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  • Chen, Xiaoli
  • Wu, Fengyan
  • Duan, Jinqiao
  • Kurths, Jürgen
  • Li, Xiaofan

Abstract

Numerous studies have demonstrated the important role of noise in the dynamical behaviour of a complex system. The most probable trajectories of nonlinear systems under the influence of Gaussian noise have recently been studied already. However, there has been only a few works that examine how most probable trajectories in the two-dimensional system (MeKS network) are influenced under non-Gaussian stable Lévy noise. Therefore, we discuss the most probable trajectories of a two-dimensional model depicting the competence behaviour in B. subtilis under the influence of stable Lévy noise. On the basis of the Fokker-Planck equation, we describe the noise-induced most probable trajectories of the MeKS network from the low ComK protein concentration (vegetative state) to the high ComK protein concentration (competence state) under stable Lévy noise. We demonstrate choices of the non-Gaussianity index α and the noise intensity ϵ which generate the ComK protein escape from the low concentration to the high concentration. We also reveal the optimal combination of both parameters α and ϵ making the tipping time shortest. Moreover, we find that different initial concentrations around the low ComK protein concentration evolve to a metastable state, and provide the optimal α and ϵ such that the distance between the deterministic competence state and the metastable state is smallest.

Suggested Citation

  • Chen, Xiaoli & Wu, Fengyan & Duan, Jinqiao & Kurths, Jürgen & Li, Xiaofan, 2019. "Most probable dynamics of a genetic regulatory network under stable Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 425-436.
  • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:425-436
    DOI: 10.1016/j.amc.2018.12.005
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    References listed on IDEAS

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    1. Gao, Ting & Duan, Jinqiao & Li, Xiaofan, 2016. "Fokker–Planck equations for stochastic dynamical systems with symmetric Lévy motions," Applied Mathematics and Computation, Elsevier, vol. 278(C), pages 1-20.
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    3. Niraj Kumar & Abhyudai Singh & Rahul V Kulkarni, 2015. "Transcriptional Bursting in Gene Expression: Analytical Results for General Stochastic Models," PLOS Computational Biology, Public Library of Science, vol. 11(10), pages 1-22, October.
    4. Gürol M. Süel & Jordi Garcia-Ojalvo & Louisa M. Liberman & Michael B. Elowitz, 2006. "An excitable gene regulatory circuit induces transient cellular differentiation," Nature, Nature, vol. 440(7083), pages 545-550, March.
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    Cited by:

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    4. Han, Ping & Wang, Liang & Xu, Wei & Zhang, Hongxia & Ren, Zhicong, 2021. "The stochastic P-bifurcation analysis of the impact system via the most probable response," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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    8. Hao, Mengli & Jia, Wantao & Wang, Liang & Li, Fuxiao, 2022. "Most probable trajectory of a tumor model with immune response subjected to asymmetric Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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