The invention includes a method for predicting the operational state of equipment with turbulent flow characterized by time series data relating to its operation. The invention further includes a system and method for predicting the onset of an impending oscillatory instability. Further, the invention includes a system and method for identifying an impending absorbing transition such as flame blowout in combustion systems. A variable representing the dynamics of operation is measured with the help of a sensor, to obtain time series data. A complex network is then derived from the measured time series data. Network properties are then calculated using the complex network to identify the state of stability relating to operation of the equipment. The stability information may include one of thermoacoustic instability, aero-elastic instability such as flutter, flow-induced vibration, magneto-hydrodynamic, aerodynamic, aeromechanical, aero-acoustic instability or onset of flame blowout of a combustor.