In this work, we numerically investigate the dynamics of a prototypical thermoacoustic system, the generalized Van der Pol oscillator, in the presence of additive noise of varying color (correlation time) and intensity while the system undergoes supercritical and subcritical Hopf bifurcation. We specifically investigate the influence of noise color on trends in the coherence factor and the Hurst exponent in the subthreshold region to assess their reliability as instability precursors. The Hurst exponent is found reliable only for correlation times much larger than the time scale of the instability while the coherence factor is found to be reliable for the entire range of noise color investigated. These inferences are found to hold for both supercritical and subcritical bifurcation cases.
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