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Interplay Between Random Fluctuations and Rate Dependent Phenomena at Slow Passage to Limit-cycle Oscillations in a Bistable Thermoacoustic System

Publication Type : Journal Article

Publisher : Chaos

Source : Chaos, Volume 29, Issue 3, p.031102 (2019)

Campus : Coimbatore

School : School of Engineering

Center : Computational Engineering and Networking

Department : Mechanical Engineering

Year : 2019

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.

Cite this Research Publication : V. R. Unni, Dr. E. A. Gopalakrishnan, Syamkumar, K. S., Sujith, R. I., Surovyatkina, E., and Kurths, J., “Interplay Between Random Fluctuations and Rate Dependent Phenomena at Slow Passage to Limit-cycle Oscillations in a Bistable Thermoacoustic System”, Chaos, vol. 29, no. 3, p. 031102, 2019.

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