Synchronization route to weak chimera in four candle-flame oscillators

Manoj, Krishna; Pawar, Samadhan A.; Dange, Suraj; Mondal, Sirshendu; Sujith, R. I.; Surovyatkina, Elena; Kurths, Jürgen

doi:10.1103/physreve.100.062204

Cited by 26 publications

(17 citation statements)

References 43 publications

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“…2018), chemical oscillators (Wang, Kiss & Hudson 2000; Kiss, Zhai & Hudson 2005) and candle-flame oscillators (Manoj et al. 2019; Manoj, Pawar & Sujith 2021). The phase difference for each of the six oscillator-pair combinations remains largely constant in time (figure 3( d 1)), indicating that the pressure oscillations in the entire network are not only frequency locked but also phase locked (Pikovsky et al.…”

Section: Resultsmentioning

confidence: 99%

“…2017), electrochemical oscillators (Bick, Sebek & Kiss 2017) and candles (Manoj et al. 2019). To date, however, weak chimeras have yet to be observed in a thermoacoustic system, where mutually constructive interactions between HRR sources and their surrounding acoustic field can give rise to destructive self-excited flow oscillations (Lieuwen & Yang 2005).…”

Section: Introductionmentioning

confidence: 99%

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Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

et al. 2022

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We take a complex systems approach to investigating experimentally the collective dynamics of a network of four self-excited thermoacoustic oscillators coupled in a ring. Using synchronization metrics, we find a wide variety of emergent multi-scale behaviour, such as (i) a transition from intermittent frequency locking on a $\mathbb {T}^{3}$ quasiperiodic attractor to a breathing chimera, (ii) a two-cluster state of anti-phase synchronization on a periodic limit cycle, and (iii) a weak anti-phase chimera. We then compute the cross-transitivity from recurrence networks to identify the dominant direction of the coupling between the heat-release-rate ( $q^{\prime }_{\mathbb {X}}$ ) and pressure ( $p^{\prime }_{\mathbb {X}}$ ) fluctuations in each individual oscillator, as well as that between the pressure ( $p^{\prime }_{\mathbb {X}}$ and $p^{\prime }_{\mathbb {Y}}$ ) fluctuations in each pair of coupled oscillators. We find that networks of non-identical oscillators exhibit circumferentially biased $p^{\prime }_{\mathbb {X}}$ – $p^{\prime }_{\mathbb {Y}}$ coupling, leading to mode localization, whereas networks of identical oscillators exhibit globally symmetric $p^{\prime }_{\mathbb {X}}$ – $p^{\prime }_{\mathbb {Y}}$ coupling. In both types of networks, we find that the $p^{\prime }_{\mathbb {X}}$ – $q^{\prime }_{\mathbb {X}}$ coupling can be symmetric or asymmetric, but that the asymmetry is always such that $q^{\prime }_{\mathbb {X}}$ exerts a greater influence on $p^{\prime }_{\mathbb {X}}$ than vice versa. Finally, we show through a cluster analysis that the $p^{\prime }_{\mathbb {X}}$ – $p^{\prime }_{\mathbb {Y}}$ interactions play a more critical role than the $p^{\prime }_{\mathbb {X}}$ – $q^{\prime }_{\mathbb {X}}$ interactions in defining the collective dynamics of the system. As well as providing new insight into the interplay between the $p^\prime_{\mathbb{X}}\text{--}p^\prime_{\mathbb{Y}}$ and $p^\prime_{\mathbb{X}}\text{--}q^\prime_{\mathbb{X}}$ coupling, this study shows that even a small network of four ring-coupled thermoacoustic oscillators can exhibit a wide variety of collective dynamics. In particular, we present the first evidence of chimera states in a minimal network of coupled thermoacoustic oscillators, paving the way for the application of oscillation quenching strategies based on chimera control.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

et al. 2022

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“…It is also reported that two-or-more oscillating flames can synchronize according to the spatial arrangement of fuel inlets [8]. The transitions between various synchronization modes have been observed [8,[16][17][18][24][25][26][27][28][29][30][31][32] and have also been investigated using mathematical models [8,24].…”

Section: Introductionmentioning

confidence: 95%

Bifurcation structure of the flame oscillation

Araya,

Ito,

Kitahata

2021

Preprint

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A flame exhibits a limit-cycle oscillation, which is called "flame flickering" or "puffing", in a certain condition. We investigated the bifurcation structure of the flame oscillation in both simulation and experiment. We performed a two-dimensional hydrodynamic simulation by employing the flame sheet model. We reproduced the flame oscillation and investigated the parameter dependences of the amplitude and frequency on the fuel-inlet diameter. We also constructed an experimental system, in which we could finely vary the fuel-inlet diameter, and investigated the diameter-dependences of the amplitude and frequency. In our simulation, we observed the hysteresis and bistability of the stationary and oscillatory states. In our experiments, we observed the switching between the stationary and oscillatory states. Therefore, we concluded that the oscillatory state appeared from the stationary state through the subcritical Hopf bifurcation in both the simulation and experiment. The amplitude was increased and the frequency was decreased as the fuel-inlet diameter was increased. In addition, we visualized the vortex structure in our simulation and discussed the effect of the vortex on the flame dynamics.

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“…The occurrence of chimera or solitary states have been designed through experimental setup comprising Huygens clock mechanical oscillators [43], coupled candle-flame oscillators via quenching and clustering [44], modular networks of electrochemical oscillations [45], and locally and non-locally coupled Stuart-Landau oscillator circuits [46]. Furthermore, machine learning techniques have been successfully being applied for prediction of system properties or emergent phenomena covering a broad areas of interdisciplinary research which ranges from non-linear dynamics, quantum physics, astrophysics to bio-medics [47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Assisted Chimera and Solitary States in Networks

et al. 2021

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Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial systems. It has been further demonstrated that such states can be engineered in systems of coupled oscillators by suitable implementation of communication delays. Here, using supervised machine learning, we predict (a) the precise value of delay which is sufficient for engineering chimera and solitary states for a given set of system's parameters, as well as (b) the intensity of incoherence for such engineered states. Ergo, using few initial data points we generate a machine learning model which can then create a more refined phase plot as well as by including new parameter values. We demonstrate our results for two different examples consisting of single layer and multi layer networks. First, the chimera states (solitary states) are engineered by establishing delays in the neighboring links of a node (the interlayer links) in a 2-D lattice (multiplex network) of oscillators. Then, different machine learning classifiers, K-nearest neighbors (KNN), support vector machine (SVM) and multi-layer perceptron neural network (MLP-NN) are employed by feeding the data obtained from the network models. Once a machine learning model is trained using the limited amount of data, it predicts the precise value of critical delay as well as the intensity of incoherence for a given unknown systems parameters values. Testing accuracy, sensitivity, and specificity analysis reveal that MLP-NN classifier is better suited than Knn or SVM classifier for the predictions of parameters values for engineered chimera and solitary states. The technique provides an easy methodology to predict critical delay values as well as intensity of incoherence for that delay value for designing an experimental setup to create solitary and chimera states.

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Synchronization route to weak chimera in four candle-flame oscillators

Cited by 26 publications

References 43 publications

Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

Bifurcation structure of the flame oscillation

Machine Learning Assisted Chimera and Solitary States in Networks

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