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Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise

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Abstract

Tipping is a phenomenon in multistable systems where small changes in inputs cause huge changes in outputs. When the parameter varies within a certain time scale, the rate will affect the tipping behaviors. These behaviors are undesirable in thermoacoustic systems, which are widely used in aviation, power generation and other industries. Thus, this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises. Transient dynamical behaviors for the proposed thermoacoustic model are implemented through the reduced Fokker-Planck-Kolmogorov equation derived by a standard stochastic averaging method. Then, the tipping problems of the rate-dependent thermoacoustic systems with random fluctuations are studied by virtue of the obtained probability density functions. Our results show that the rate delays the value of the tipping parameter compared to the one with the quasi-steady assumption, which is called as a rate-dependent tipping-delay phenomenon. Besides, the influences of the initial values, the rate, the changing time of the parameters, and the correlation time of the noises on the rate-dependent tipping-delay phenomenon are analyzed in detail. These results are of great significance for research in related fields such as aviation and land gas turbines.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    XiaoYu Zhang, Yong Xu & Qi Liu

  2. MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an, 710072, China

    Yong Xu

  3. Potsdam Institute for Climate Impact Research, Potsdam, 14412, Germany

    Jürgen Kurths

Authors
  1. XiaoYu Zhang
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  2. Yong Xu
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  3. Qi Liu
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  4. Jürgen Kurths
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Corresponding author

Correspondence to Yong Xu.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 11772255), the Fundamental Research Funds for the Central Universities, the Research Funds for Interdisciplinary Subject of Northwestern Polytechnical University, the Shaanxi Project for Distinguished Young Scholars, and Shaanxi Provincial Key R&D Program (Grant Nos. 2020KW-013 and 2019TD-010).

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Zhang, X., Xu, Y., Liu, Q. et al. Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise. Sci. China Technol. Sci. 63, 2315–2327 (2020). https://doi.org/10.1007/s11431-020-1589-x

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  • DOI: https://doi.org/10.1007/s11431-020-1589-x

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