Tipping in complex systems under fast variations of parameters

Abstract

Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced 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 show that another system parameter, not under our control, changes simultaneously at a different rate, and the competition between the effects of that parameter and the control parameter determines if and when tipping occurs. Motivated by the experiments, we use a nonlinear oscillator model exhibiting Hopf bifurcation to generalize this tipping to complex systems in which slow and fast parameters compete to determine the system dynamics.