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Time delay effects of stochastic resonance induced by multiplicative periodic signal in the gene transcriptional regulatory model

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  • Bai, Chunyan

Abstract

Based on the universal transcriptional regulatory model proposed by Smolen et al.in 1998, we have studied the combined effects of cross-correlation noise, multiplicative periodic signal and time delay through modifying the ordinary differential equation with time evolution in gene transcriptional regulatory system. The expression of signal-to-noise ratio (SNR) is derived by applying the two-state theory in adiabatic limit and approximate analytical method for small time delay. The effects of multiplicative noise intensity, additive noise intensity, cross-correlation noise intensity and time delay on SNR are discussed by numerical calculation and graphical analysis. The results indicate that when the SNR is a function of multiplicative noise intensity, the peak value of the SNR rises as time delay increases; when SNR is a function of additive noise intensity, the value of SNR ascends as time delay increases; when SNR is a function of cross-correlation noise intensity, the peak value of SNR goes up with time delay increased. So when SNR is the function of multiplicative noise intensity, additive noise intensity and cross-correlation noise intensity respectively, time delay enhances the stochastic resonance.

Suggested Citation

  • Bai, Chunyan, 2018. "Time delay effects of stochastic resonance induced by multiplicative periodic signal in the gene transcriptional regulatory model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 304-311.
    • Handle: RePEc:eee:phsmap:v:507:y:2018:i:c:p:304-311
    DOI: 10.1016/j.physa.2018.05.025
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    Cited by:

    1. Duan, Wei-Long, 2020. "The stability analysis of tumor-immune responses to chemotherapy system driven by Gaussian colored noises," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Duan, Wei-Long & Lin, Ling, 2021. "Noise and delay enhanced stability in tumor-immune responses to chemotherapy system," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Bi, Haohao & Lei, Youming & Han, Yanyan, 2019. "Stochastic resonance across bifurcations in an asymmetric system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1296-1312.

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