Tipping in complex systems under fast variations of parameters

TL;DR

This paper experimentally demonstrates rate-induced tipping in a real-world complex system, revealing how competing parameters and their rates of change can trigger sudden state transitions.

Contribution

It provides the first experimental evidence of rate-induced tipping in a real system and introduces a nonlinear oscillator model to analyze the interplay of multiple changing parameters.

Findings

Critical rate of parameter change induces tipping

Competing parameter effects influence tipping occurrence

Model generalizes to complex systems with fast and slow 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.