Intermittency observed prior to thermoacoustic instability is characterized by the occurrence of bursts of high-amplitude periodic oscillations (active state) amidst epochs of low-amplitude aperiodic fluctuations (rest state). Several model-based studies conjectured that bursting arises due to the underlying turbulence in the system. However, such intermittent bursts occur even in laminar and low-turbulence combustors, which cannot be explained by models based on turbulence. We assert that bursting in such combustors may arise due to the existence of subsystems with varying timescales of oscillations, thus forming slow–fast systems. Experiments were performed on a horizontal Rijke tube and the effect of slow–fast oscillations was studied by externally introducing low-frequency sinusoidal modulations in the control parameter. The induced bursts display an abrupt transition between the rest and the active states. The growth and decay patterns of such bursts show asymmetry due to delayed bifurcation caused by slow oscillations of the control parameter about the Hopf bifurcation point. Further, we develop a phenomenological model for the interaction between different subsystems of a thermoacoustic system by either coupling the slow and fast subsystems or by introducing noise in the absence of slow oscillations of the control parameter. We show that interaction between subsystems with different timescales leads to regular amplitude modulated bursting, while the presence of noise induces irregular amplitude modulations in the bursts. Thus, we speculate that bursting in laminar and low-turbulence systems occurs predominantly due to the interdependence between slow and fast oscillations, while bursting in high-turbulence systems is predominantly influenced by the underlying turbulence.
We report the first experimental evidence of strange nonchaotic attractor (SNA) in the natural dynamics of a self-excited laboratory-scale system. In the previous experimental studies, the birth of SNA was observed in quasiperiodically forced systems; however, such an evidence of SNA in an autonomous laboratory system is yet to be reported. We discover the presence of SNA in between the attractors of quasiperiodicity and chaos through a fractalization route in a laboratory thermoacoustic system. The observed dynamical transitions from order to chaos via SNA is confirmed through various nonlinear characterization methods prescribed for the detection of SNA.Coupled nonlinear systems exhibit various kinds of dynamical behaviours including periodic, quasiperiodic, and chaotic oscillations [1,2]. Among these dynamics, one of the commonly observed state in quasiperiodically driven nonlinear systems is a strange nonchaos. Although strange nonchaotic attractors (SNAs) show similarity to chaotic attractors by having a fractal geometrical structure, SNAs are insensitive to initial conditions unlike the chaotic attractors [3]. Grebogi et al. [4] was the first to report the possibility of SNAs in the system of quasiperiodically forced map. Afterwards, several numerical studies have demonstrated the existence of SNAs in systems such as pendulum [5], Duffing oscillator [6], logistic map [7], Henon map [8], and circular map [9].The experimental discovery of SNA was reported by Ditto et al.[10] in a quasiperiodically forced system with a buckled magnetoelastic ribbon. In subsequent years, there have been several experimental observations of SNAs in practical systems [11][12][13][14][15]; however, all these studies presented the necessity of having quasiperiodic forcing to generate SNAs. Contrary to these studies, Negi et al. [16] showed theoretically that the need of quasiperiodic forcing is not mandatory for the creation of SNAs, and it could happen in naturally driven systems as well without the need of external forcing. Recently, Lindner et al. [17] showed the observation of SNAs in the natural system of a pulsating star KIC 5520878 network. However, to the best of our knowledge, there has not been a single experimental evidence of SNA reported in self-driven laboratory systems until now.Most of the recent studies are focused on identifying the routes to generate SNAs [3,12,18]. The mechanisms for the onset of SNAs are usually classified into three types as: (i) Heagy-Hammel route -the SNAs emerges during the collision of a period doubled torus with its own unstable parent [19], (ii) fractalization route -the truncated torus gets wrinkled and forms SNAs without any interaction with the parent torus [20], and (iii) type-III intermittency route -SNAs occur when the torus doubling bifurcation is controlled by sub-harmonic bifurcations [6]. Another possibility for the occurrence of SNAs is through crisis-induced intermittency, wherein the collision of the wrinkled torus with the boundary results in sudden widening of the attra...
Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.
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