  A sudden transition to a state of high amplitude limit cycle oscillations is
catastrophic in a thermo-fluid system. Conventionally, upon varying the control
parameter, a sudden transition is observed as an abrupt jump in the amplitude
of the fluctuations in these systems. In contrast, we present an experimental
discovery of a canard explosion in a turbulent reactive flow system where we
observe a continuous bifurcation with a rapid rise in the amplitude of the
fluctuations within a narrow range of control parameters. The observed
transition is facilitated via a state of bursting, consisting of the epochs of
large amplitude periodic oscillations amidst the epochs of low amplitude
periodic oscillations. The amplitude of the bursts is higher than the amplitude
of the bursts of intermittency state in a conventional gradual transition, as
reported in turbulent reactive flow systems. During the bursting state, we
observe that temperature fluctuations of exhaust gas vary at a slower time
scale in correlation with the amplitude envelope of the bursts. We also present
a phenomenological model for thermoacoustic systems to describe the observed
canard explosion. Using the model, we explain that the large amplitude bursts
occur due to the slow-fast dynamics at the bifurcation regime of the canard
explosion.
