Unni, Vishnu R. ; Gopalakrishnan, E. A. ; Syamkumar, K. S. ; Sujith, R. I. ; Surovyatkina, Elena ; Kurths, Jürgen (2019) Interplay between random fluctuations and rate dependent phenomena at slow passage to limit-cycle oscillations in a bistable thermoacoustic system Chaos, 29 (3). 031102. ISSN 1054-1500
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Official URL: http://doi.org/10.1063/1.5088943
Related URL: http://dx.doi.org/10.1063/1.5088943
Abstract
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.
Item Type: | Article |
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Source: | opyright of this article belongs to American Institute of Physics. |
ID Code: | 124470 |
Deposited On: | 22 Nov 2021 10:24 |
Last Modified: | 22 Nov 2021 10:24 |
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