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Influence of non-Gaussian noise on the coherent feed-forward loop with time delay

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  • Wang, Min
  • Fang, Yuwen
  • Luo, Yuhui
  • Yang, Fengzao
  • Zeng, Chunhua
  • Duan, Wei-Long

Abstract

The effect of non-Gaussian noise on the coherent feed-forward loop with time delay is researched. Based on delayed Fokker–Planck equation, the expressions of the steady-state probability distribution, mean, normalized variance, normalized skewness, and normalized kurtosis of concentration variables y and z of two transcription factors X, Y and a target gene Z in the model are derived. Then, the impacts of the noise intensity D, parameter q indicating the departure from Gaussian noise, correlation time τ0 of non-Gaussian noise, and time delay τ on the steady-state probability distribution, mean, normalized variance, skewness, and kurtosis are discussed. The results show that, non-Gaussian noise will weaken the stability of Y and Z, increase the concentration of y and z, and ultimately benefit the output of target gene Z. Time delay also weaken the stability of Y and Z, but increase the concentrations of y and decrease the concentrations of z, i.e., suppress the output of target gene Z. In addition, numerical simulations are performed and consistent with approximate theoretical results.

Suggested Citation

  • Wang, Min & Fang, Yuwen & Luo, Yuhui & Yang, Fengzao & Zeng, Chunhua & Duan, Wei-Long, 2019. "Influence of non-Gaussian noise on the coherent feed-forward loop with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 46-55.
    • Handle: RePEc:eee:chsofr:v:129:y:2019:i:c:p:46-55
    DOI: 10.1016/j.chaos.2019.07.047
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