Effect of noise amplification during the transition to amplitude death in coupled thermoacoustic oscillators

Abstract

We present a systematic investigation of the effect of external noise on the dynamics of a system of two coupled prototypical thermoacoustic oscillators, horizontal Rijke tubes, using a mathematical model. We focus on the possibility of amplitude death (AD), which is observed in the deterministic model of coupled thermoacoustic oscillators as studied by Thomas et al. [Chaos 28, 033119 (2018)], in the presence of noise. Although a complete cessation of oscillations or AD is not possible in the stochastic case, we observe a significant reduction in the amplitude of coupled limit cycle oscillations (LCOs) with the application of strong coupling. Furthermore, as we increase the noise intensity, a sudden drop in the amplitude of pressure oscillations at the transition from LCO to AD, observed in the noise free case, is no longer discernible because of the amplification of noise in AD state. During this transition from LCO to AD, we notice a qualitative change in the distribution of the pressure amplitude from bimodal to unimodal. Furthermore, in order to demarcate the boundary of the transition from LCO and AD in the noisy case, we use 80 % suppression in the amplitude of LCO, which generally occurs in the parameter range over which this qualitative change in the pressure distribution happens, as a threshold. With the help of bifurcation diagrams, we show a qualitative change as well as a reduction in the size of amplitude suppression zones that happen due to the increase in noise intensity. We also observe the relative ease of suppressing the amplitude of LCO with time-delay coupling when detuning and dissipative couplings are introduced between the two thermoacoustic oscillators in the presence of noise.