Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
11 Downloads (Pure)


Thermoacoustic instability has been an important challenge in the development of highperformance combustion systems, as it can have catastrophic consequences. The process of a sudden change in the dynamical behaviour of a thermoacoustic system from a low to a high amplitude thermoacoustic instability, actually entails as a tipping point phenomenon. It has been found that when rate-dependent parameters are considered, a tipping-delay phenomenon may arise, which helps in the control of undesirable states that give rise to thermoacoustic instabilities. This work aims at understanding rate-dependent tipping dynamics of the thermoacoustic system with both time-varying parameters and a non-Gaussian L´evy noise. The latter better describes the severe operating environment of such systems than simpler types of noise. Through numerical simulations, the tipping dynamical behaviour is analysed by considering the rate-dependent parameters coupled with the main parameters
of the L´evy noise, including the stability and skewness indices, and the noise intensity. In addition, we investigate the effectiveness of early warning indicators in rate-dependent systems under L´evy noise excitation, and uncover a relationship between warning measures and the rate of change in the parameters. These results inform and enlighten the development and design of power combustion devices, and also provide researchers and engineers with
effective ideas to control thermoacoustic instability and the associated tipping dynamics.
Original languageEnglish
Article number113115
Number of pages15
Issue number11
Early online date9 Nov 2021
Publication statusPublished - Nov 2021

Bibliographical note

This work was partly supported by the NSF of China (12072264), the Key International (Regional) Cooperative Research Projects of the NSF of China (12120101002), the Research Funds for Interdisciplinary Subject of NPU, the Shaanxi Provincial Key R&D Program (Grants 2020KW-013, 2019TD-010)


  • Thermoacoustic instability
  • L´evy noise
  • Rate-dependent tipping
  • early warning


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