Critical Transitions are sudden changes in the dynamics of complex sistems, often with catastrophic consequences. There are several mechanism leading to a critical transition and we focus on those caused by the rate of a time-dependent drift of parameters  (which are usually fixed or at most varied adabatically), so-called rate-induced tipping.
Particularly, in the case of a rate-induced tipping, a system evolves in time into another with posibly same topological properties of stability. However, depending on the rate at which such transition takes place , a local attractor of the past system  can fall to track  the corresponding  local attractor of the future system. This encompasses various real scenarios, for example in ecology, climate, biology and quantum mechanics. 