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

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 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 and pressure fluctuations in each individual oscillator, as well as that between the pressure (and) fluctuations in each pair of coupled oscillators. We find that networks of non-identical oscillators exhibit circumferentially biased - coupling, leading to mode localization, whereas networks of identical oscillators exhibit globally symmetric - coupling. In both types of networks, we find that the - coupling can be symmetric or asymmetric, but that the asymmetry is always such that exerts a greater influence on than vice versa. Finally, we show through a cluster analysis that the - interactions play a more critical role than the - interactions in defining the collective dynamics of the system. As well as providing new insight into the interplay between the and 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.