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. The thermoacoustic instability may lead to the disintegration of rocket engines, gas turbines and aeroengines, as well as other serious irreversible consequences. Thus, this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the Lévy noise. 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. In addition, the influence of the index of stability, skewness parameter and noise intensity on tipping delay is analyzed in detail. These results are of great significance for research in related fields such as aviation and land gas turbines.
 

Thermoacoustic system; Lévy noise; Rate-dependent tipping; Transient