Reliability of early warning indicators of critical transition in stochastic Van der Pol oscillators with additive correlated noise

We conduct a numerical investigation to assess the effect of noise characteristics on early warning indicators (EWIs) of critical transition in Van der Pol oscillators undergoing supercritical and subcritical Hopf bifurcation. Our study primarily focuses on the effects of additive correlated noise modeled by the OU process in the stable (subthreshold) region and corresponding trends in EWIs based on signal amplitude distribution, frequency spectra, fractal, and complexity measures as the system is brought closer to bifurcation, as a function of noise color and intensity. Our results indicate that the coherence factor is a reliable indicator for the entire range of investigated noise color, while variance and decay rates of the autocorrelation function are reliable when noise correlation times are either much smaller or larger than the system time scale. Kurtosis, permutation entropy and Jensen-Shannon complexity can be effectively employed in systems where noise exhibits minimal correlation time (resembling white noise). While the Hurst exponent proves a reliable indicator in systems where noise has correlation times much larger than the time scale of the system, multi-fractal spectrum width and skewness are deemed unsuitable as EWIs. These insights enhance our understanding of the effectiveness and limitations of various EWIs in forecasting critical transitions within dynamical systems.