We experimentally study the dynamical state and driving region of combustion instability in a turbulent combustor under low- and high-swirling flow conditions by the complex-systems approach. As the swirl number is increased, the combustion state undergoes a transition from stable combustion to complex combustion instability with large-amplitude modulations via low- and high-amplitude combustion instability. A chaotic state emerges during combustion instability with large-amplitude modulations. A symbolic dynamics-based thermoacoustic power network can identify the emergence of the thermoacoustic power source during combustion instability. The driving region of combustion instability can be clearly extracted from the symbolic dynamics-based synchronization index and the local node entropy in the Rayleigh index-based transition network. Reservoir computing has a potential use in clarifying the phase synchronized state between acoustic pressure and heat release rate fluctuations during the chaotic state in combustion instability with large-amplitude modulations.
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