Liquid rocket engines are prone to transverse instabilities that can lead to delays at the development stage or catastrophic engine failures in flight. In this seminar, we present the results from our study on the coupled interaction between the transverse acoustic pressure and the heat release rate oscillations in a model multi-element liquid rocket engine combustor based on oxidizer rich staged combustiuon cycle. We also study the other dynamical states preceding thermoacoustic instability. We analyze the coupled dynamics both from a global analysis using time series data as well as a local analysis using spatially resolved images. Using tools from synchronization theory, we quanitify the coupled behavior between acoustic pressure and heat release rate oscillations during the dynamical states of stable state, intermittency and thermoacoustic instability. Based on concepts from recurrence theory, we also distinguish the type of synchronization between the acoustic pressure and the global heat release rate oscillations at the wall and the center of the combustor during thermoacoustic instability. Further, we characterize the behavior of the local heat release rate oscillations and the influence of the acoustic shockwave in its dynamics. We believe that the understanding of the coupled behavior between the acoustics and the heat release rate oscillations during the transition from stable state to thermoacoustic instability can be useful for models and high-fidelity simulations of combustion dynamics in the multi element combustors of liquid rocket engines.