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