Changing parameters yield insight into early warning signals for critical transitions
Changing parameters yield insight into early warning signals for critical transitions lead image
Dynamical systems often exhibit critical transitions, where a small change in input dramatically alters the state of the system. Accurately predicting the location and intensity of these transitions is difficult because they often depend on the value and rate of change of control parameters, as well as noise present in the system.
Induja Pavithran and R.I. Sujith evaluate several early warning signals that might anticipate critical transitions. By continuously varying input parameters, they find that two kinds of signals, lag-1 autocorrelation and the Hurst exponent, outperform other tested signals, and the warning times of these signals fall as inputs change faster.
“Most of the earlier studies have considered quasi-steady variation of the parameter,” said Sujith. “Since we have considered the continuous variation of parameter at different rates, we were able to find that warning time for critical transitions reduces with the rate of change of parameter following an inverse power law scaling.”
The group examined critical transitions in a thermoacoustic system known as a Rijke tube, an open-ended hollow tube containing a metal mesh. Passing current through the mesh heats the air inside, changing its pressure and driving a standing wave, which is very dangerous in real combustion systems. Therefore, an early warning is so crucial.
The group measured the acoustic pressure inside the tube as a function of applied voltage. By varying the power passed through the grate, they observed bifurcation induced tipping in the system.
“The inherent noise or fluctuations present in the system considered in this study is relatively low,” said Sujith. “For our next study, we are planning to look at the combined effects of noise and rate of change of parameter on critical transitions.”
Source: “Effect of rate of change of parameter on early warning signals for critical transitions,” by Induja Pavithran and R. I. Sujith, Chaos (2020). The article can be accessed at https://doi.org/10.1063/5.0025533 .
