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

Abstract

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 T3 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′X ) and pressure ( p′X ) fluctuations in each individual oscillator, as well as that between the pressure ( p′X and p′Y ) fluctuations in each pair of coupled oscillators. We find that networks of non-identical oscillators exhibit circumferentially biased p′X – p′Y coupling, leading to mode localization, whereas networks of identical oscillators exhibit globally symmetric p′X – p′Y coupling. In both types of networks, we find that the p′X – q′X coupling can be symmetric or asymmetric, but that the asymmetry is always such that q′X exerts a greater influence on p′X than vice versa. Finally, we show through a cluster analysis that the p′X – p′Y interactions play a more critical role than the p′X – q′X interactions in defining the collective dynamics of the system. As well as providing new insight into the interplay between the p′X--p′Y and p′X--q′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.