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Delay-induced transitions in the birhythmic biological model under joint noise sources

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  • Guo, Qin
  • Sun, Zhongkui
  • Xu, Wei

Abstract

In this paper, the combined effects of delayed feedbacks and noise on the enzyme–substrate reaction in the brain are examined. By means of the approximate methods, we analyze the stationary probability density function of the amplitude and the joint of displacement and velocity, finding that stochastic bifurcations can be induced by noise correlation and time delay. In Particular, the system undergoes a succession of two transitions as time delay is varied monotonically, namely, the reentrance phenomenon appears. The analytical results appear to be in reasonable agreement with the direct numerical simulations of the original system. From the biological point of view, the reaction rate of the enzymatic substrate reaction can be enhanced or diminished by Gaussian colored noise. More intriguingly, an increase in displacement feedback will retard the reaction rate, nevertheless, whether an increasing velocity feedback will benefit the reaction rate depends on time delay. It is worth noting that the chemical oscillations can be controlled to a low level when the appropriate time delay is chosen.

Suggested Citation

  • Guo, Qin & Sun, Zhongkui & Xu, Wei, 2019. "Delay-induced transitions in the birhythmic biological model under joint noise sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 337-348.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:337-348
    DOI: 10.1016/j.physa.2019.03.047
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    References listed on IDEAS

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    1. Sun, Zhongkui & Xu, Wei & Yang, Xiaoli & Fang, Tong, 2007. "Effects of time delays on bifurcation and chaos in a non-autonomous system with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 39-53.
    2. Yonkeu, R. Mbakob & Yamapi, R. & Filatrella, G. & Tchawoua, C., 2017. "Effects of a periodic drive and correlated noise on birhythmic van der Pol systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 552-569.
    3. Wang, Can-Jun & Yang, Ke-Li & Du, Chun-Yan, 2017. "Multiple cross-correlation noise induced transition in a stochastic bistable system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 261-274.
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    5. Paul M. Geffert & Anna Zakharova & Andrea Vüllings & Wolfram Just & Eckehard Schöll, 2014. "Modulating coherence resonance in non-excitable systems by time-delayed feedback," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(12), pages 1-13, December.
    6. Wu, Dan & Luo, Xiaoqin & Zhu, Shiqun, 2007. "Stochastic system with coupling between non-Gaussian and Gaussian noise terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 203-214.
    7. Sun, Zhongkui & Xu, Wei & Yang, Xiaoli & Fang, Tong, 2006. "Inducing or suppressing chaos in a double-well Duffing oscillator by time delay feedback," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 705-714.
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    Cited by:

    1. Fu, Peng & Wang, Can-Jun & Yang, Ke-Li & Li, Xu-Bo & Yu, Biao, 2022. "Reentrance-like vibrational resonance in a fractional-order birhythmic biological system," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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