Transient response and stochastic bifurcation of a Rijke tube model based on path integral method

The noise-induced dynamics are of paramount importance in thermoacoustic systems due to the ubiquity of noise in various practical combustion systems. However, the intrinsic mechanisms of noise-induced dynamics are usually too complicated to conduct an exhaustive investigation. In this study, we conduct a detailed investigation on the transient response and stochastic bifurcation in a Rijke tube model based on the path integral method. This study suggest that the heater power and time delay can induce stochastic P-bifurcation, while noise intensity cannot induce stochastic P-bifurcation, and only has a slight quantitative effect on the stationary probability density function. All these findings will be beneficial to the theoretical research of noise-induced transitions and the practical guidance for the design of thermoacoustic devices in the presence of noise.