Tipping in complex systems under fast variations of parameters

Abstract

Abrupt changes in the state of a system are often undesirable in natural and human-made systems. Such transitions occurring due to fast variations of system parameters are called rate-induced tipping (R-tipping). While a quasi-steady or sufficiently slow variation of a parameter does not result in tipping, a continuous variation of the parameter at a rate greater than a critical rate results in tipping. Such R-tipping would be catastrophic in real-world systems. We experimentally demonstrate R-tipping in a real-world complex system and decipher its mechanism. There is a critical rate of change of parameter above which the system undergoes tipping. We discover that there is another system variable varying simultaneously at a timescale different from that of the driver (control parameter). The competition between the effects of processes at these two timescales determines if and when tipping occurs. Motivated by the experiments, we use a nonlinear oscillator model, exhibiting Hopf bifurcation, to generalize such type of tipping to complex systems where multiple comparable timescales compete to determine the dynamics. We also explain the advanced onset of tipping, which reveals that the safe operating space of the system reduces with the increase in the rate of variations of parameters.