  Self-sustained order can emerge in complex systems due to internal feedback
between coupled subsystems. Here, we present our discovery of a non-monotonic
emergence of order amidst chaos in a turbulent thermo-acoustic fluid system.
Fluctuations play a vital role in determining the dynamical state and
transitions in a system. In this work, we use complex networks to encode jumps
in amplitude scales owing to fluctuations as links between nodes representing
amplitude bins. The number of possible amplitude transitions at a fixed
timescale reflects the complexity of dynamics at that timescale. The network
entropy quantifies the number of and uncertainty associated with such
transitions. Using network entropy, we show that the uncertainty in
fluctuations first increases and then decreases as the system transitions from
chaos via intermittency to order. The competition between turbulence and
nonlinear interactions leads to such non-monotonic emergence of order amidst
chaos in turbulent thermo-acoustic fluid systems.
