Stochastic bifurcations and its regulation in a Rijke tube model

This paper explores the stochastic dynamics in a Rijke tube model. Dynamical model is established to identify the bifurcation properties of the Rijke tube model. We gain the analytical expression of the local Hopf bifurcation and global saddle-node bifurcation of the limit cycle in the deterministic case. The stationary probability density function (PDF) of the model is attained base on the method of stochastic average in the case of stochasticity. The investigations indicate that the stationary PDF switches from unimodal shape to bimodal one, and then, from bimodal shape to unimodal one again, when noise intensity, fractional order, time delay monotonically increase which is the typical feature of stochastic P-bifurcation. Further, we conclude that the stochastic P-bifurcation can be induced or suppressed by modulating the time delay, the noise intensity, or the fractional order. These findings of the study will be helpful to the theoretical study of thermoacoustic instability and the preliminary design of thermoacoustic devices where thermoacoustic instability is a concern.