Rate-dependent bifurcation dodging in a thermoacoustic system driven by colored noise

Xiaoyu Zhang, Yong Xu* (Corresponding Author), Qi Liu, Jürgen Kurths, Celso Grebogi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)
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Tipping in multistable systems occurs usually by varying the input slightly, resulting in the output switching to an often unsatisfactory state. This phenomenon is manifested in thermoacoustic systems. This thermoacoustic instability may lead to the disintegration of rocket engines, gas turbines and aeroengines, so it is necessary to design control measures for its suppression. It was speculated that such unwanted instability states may be dodged by changing quickly enough the bifurcation parameters. Thus, in this work, based on a fundamental mathematical model of thermoacoustic systems driven by colored noise, the corresponding Fokker-Planck-Kolmogorov equation of the amplitude is derived by using a stochastic averaging method. A transient dynamical behavior is identified through a probability density analysis. We find that the rate of change of parameters and the correlation time of the noise are helpful to dodge thermoacoustic instability, while a relatively large noise intensity is a disadvantageous factor. In addition, power-law relationships between the maximum amplitude and the noise parameters are explored, and the probability of successfully dodging a thermoacoustic instability is calculated. These results serve as a guide to the design of engines and to propose an effective control strategy, which is of great significance to aerospace-related fields.
Original languageEnglish
Pages (from-to)2733-2743
Number of pages11
JournalNonlinear Dynamics
Early online date19 Mar 2021
Publication statusPublished - 31 May 2021

Bibliographical note

This paper was supported by the National Natural Science Foundation of China under Grant No.11772255 and No.12072264, the National Key Research and Development Program of China (No. 2018AAA0102201), 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 2020KW-013 and 2019TD-010.


  • thermoacoustic system
  • colored noise
  • rate-dependent tipping
  • transient


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