Global phase-space approach to rate-induced tipping: A brief review

In nonautonomous dynamical systems, rate-induced tipping (R-tipping) is a critical transition triggered by the rate of change of a time-varying parameter, rather than its absolute value. In recent years, there is a growing interest in R-tipping due to its relevance to significant problems of current interest, such as potential, catastrophic collapse of various ecosystems induced by climate change. This brief review provides an overview of the basic concept, theory, and real-world implications of R-tipping from a global phase-space point of view. The key quantity underlying the global approach is the probability of R-tipping defined with respect to initial conditions in the phase space. A recently discovered scaling law governing this probability and the rate of parameter change is introduced, which has so far been restricted to a class of high-dimensional, complex, and empirical ecological networks: pollinator-plant mutualistic networks. Issues such as prediction of tipping and protection of ecosystems from R-tipping are discussed.