A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry

Complex systems involving multiple oscillatory components are known to exhibit emergent collective spatiotemporal patterns. The turbulent annular combustor is a prime example where the interaction between the acoustic field and the heat release rate fluctuations from multiple flames gives rise to rich spatiotemporal collective behavior. The collective dynamical behavior leads to high-amplitude, self-sustained oscillations in the acoustic field, which are detrimental to the system. In this study, we investigate the transition among various collective dynamical states, including the splay state, the two-cluster state, the in-phase state, the amplitude-modulated two-cluster state, and the quasiperiodic weak chimera, in the acoustic field of a turbulent annular combustor as the control parameter is varied. We also observe the signatures of the impending dynamical state before the transition. We introduce a network-based characterization method to characterize these dynamical states. We construct a functional network among the acoustic pressure fluctuations recorded around the annulus of the annular combustor. We show that each dynamical state has a unique network topology. Further, we demonstrate that the network-based measure can detect the impending transition between states in the annular combustor. This can potentially enable the timely implementation of control actions to prevent such transitions to the collective states.