Strange nonchaos in self-excited singing flames

Abstract

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...

Critical transitions and their early warning signals in thermoacoustic systems

“…Figure 3 shows this bifurcation diagram. Recently, the presence of strange non-chaotic oscillations was reported in the same system [31].…”

An Introduction to Dynamical Systems Theory

“…Grebogi et al [34], for the first time, identified SNA in a quasiperiodically driven dynamical system. The first experimental evidence of SNA in a self-excited system was reported by Premraj et al [72] in the self-excited dynamics of a laminar thermoacoustic system. Strange nonchaotic oscillations are mostly observed between the states of quasiperiodic and chaotic oscillations.…”

Rijke tube: A nonlinear oscillator

“…4), we witness rich dynamical behavior resulting from a secondary Hopf bifurcation of limit cycle oscillations (see Fig. 9) due to the variation of different control parameters [73][74][75]109,111,178,179,[182][183][184] . In this section, we will discuss the characteristics of these dynamical states and then elaborate different routes to chaos observed in Rijke tube systems.…”

“…These states include period-2, period-3, periodk, frequency-locked, quasiperiodic, strange nonchaotic, intermittent, and chaotic oscillations. There are many experimental as well as theoretical studies in the thermoacoustic literature that report the existence of these dynamical behaviors in Rijke tube systems 74,75,109,110,150,[177][178][179][180] . Sometimes, a secondary Hopf bifurcation observed due to a change in the control parameter leads to the transition from low amplitude limit cycle oscillations to high amplitude limit cycle oscillations, where both the limit cycle oscillations exhibit the same frequency 28 .…”