Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators. (English) Zbl 07488223
Summary: 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 \(p^\prime_{\mathbb{X}}\)-\(p^\prime_{\mathbb{Y}}\) and \(p^\prime_{\mathbb{X}}\)-\(q^\prime_{\mathbb{X}}\) 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.
MSC:
| 76-XX | Fluid mechanics |
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