  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.
