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

• Published in: Journal of fluid mechanics Vol. 938
• Main Authors: Guan, Yu, Moon, Kihun, Kim, Kyu Tae, Li, Larry K.B.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.05.2022
• Subjects: Acoustics; Asymmetry; Chimeras; Cluster analysis; Complex systems; Coupling; Dynamics; Fluctuations; Frequency locking; JFM Papers; Localization; Mode localization; Networks; Oscillators; Synchronism; Synchronization; Thermoacoustics; turbulent reacting flows; nonlinear dynamical systems; instability
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2022.130

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.