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Interplay between random fluctuations and rate dependent phenomena at slow passage to limit-cycle oscillations in a bistable thermoacoustic system
K. S. Syamkumar,
Published in American Institute of Physics Inc.
PMID: 30927835
Volume: 29
Issue: 3
We study the impact of noise on the rate dependent transitions in a noisy bistable oscillator using a thermoacoustic system as an example. As the parameter - the heater power - is increased in a quasi-steady manner, beyond a critical value, the thermoacoustic system undergoes a subcritical Hopf bifurcation and exhibits periodic oscillations. We observe that the transition to this oscillatory state is often delayed when the control parameter is varied as a function of time. However, the presence of inherent noise in the system introduces high variability in the characteristics of this critical transition. As a result, if the value of the system variable - the acoustic pressure - approaches the noise floor before the system crosses the unstable manifold, the effect of rate on the critical transition becomes irrelevant in determining the transition characteristics, and the system undergoes a noise-induced tipping to limit-cycle oscillations. The presence of noise-induced tipping makes it difficult to identify the stability regimes in such systems by using stability maps for the corresponding deterministic system. © 2019 Author(s).
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PublisherData powered by TypesetAmerican Institute of Physics Inc.
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