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.