Journal ArticleDOI
Interplay between random fluctuations and rate dependent phenomena at slow passage to limit-cycle oscillations in a bistable thermoacoustic system
Vishnu R. Unni,E. A. Gopalakrishnan,K. S. Syamkumar,R. I. Sujith,Elena Surovyatkina,Elena Surovyatkina,Jürgen Kurths +6 more
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TLDR
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.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.read more
Citations
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Journal ArticleDOI
Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise
TL;DR: In this paper, the authors considered the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises.
Journal ArticleDOI
Critical transitions and their early warning signals in thermoacoustic systems
TL;DR: In this paper, the authors highlight the importance of the inherent fluctuations in the system in providing early warning signals for critical transitions and highlight the challenges faced while detecting oscillatory instabilities in practical systems.
Journal ArticleDOI
Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise
TL;DR: In this paper, the authors considered the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises.
Journal ArticleDOI
Double excitation multi-stability and multi-pulse chaotic vibrations of a bistable asymmetric laminated composite square panels under foundation force.
TL;DR: Numerical simulations including the bifurcation diagrams, largest Lyapunov exponents, phase portraits, waveforms, and Poincaré sections are utilized to study the double excitation multi-pulse jumping and metastable chaotic vibrations and dynamic snap-through phenomena and it is verified that the bistable asymmetric laminated composite square panel with small damping is easier to producedouble excitation Shilinikov multi- pulse jumping chaotic vibrations.
Journal ArticleDOI
Effect of rate of change of parameter on early warning signals for critical transitions
Induja Pavithran,R. I. Sujith +1 more
TL;DR: In this paper, the impact of variation of the control parameter with a finite rate on the performance of early warning signals (EWS) for critical transitions in a thermoacoustic system exhibiting subcritical Hopf bifurcation was studied.
References
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Book
Nonlinear dynamics and Chaos
TL;DR: The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter, and the progression through period-doubling bifurcations to the onset of chaos is considered.
Journal ArticleDOI
The slow passage through a Hopf bifurcation: delay, memory effects, and resonance
TL;DR: In this article, the authors explored analytically and numerically in the context of the FitzHugh-Nagumo model of nerve membrane excitability, and found that the transition is realized when the parameter is considerably beyond the value predicted from a straightforward bifurcation analysis which neglects; the dynamic aspect of the parameter variation.
Journal ArticleDOI
Sensitivity and Nonlinearity of Thermoacoustic Oscillations
Matthew P. Juniper,R. I. Sujith +1 more
TL;DR: In this article, a review explains why linear and nonlinear thermoacoustic behavior is so sensitive to parameters such as operating point, fuel composition, and injector geometry, and proposes tools to exploit this sensitivity in the future: adjoint-based sensitivity analysis to optimize passive control designs and complex systems theory to warn of impending thermo-acoustic oscillations and to identify the most sensitive elements of a thermo acoustic system.
Journal ArticleDOI
Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition
TL;DR: In this article, a procedure is developed to find the lowest initial energy that can trigger self-sustained oscillations, as well as the corresponding initial state, known as the "most dangerous" initial state.
DissertationDOI
Thermoacoustic instabilities in the Rijke tube: experiments and modeling
TL;DR: In this paper, an electrically heated, horizontally oriented, Rijke tube is used for the experimental study of transition to instability and a theory that explains and predicts the effects observed.
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