The role of different timescales in critical transitions

Abstract

Critical transitions, relatively sudden transitions between qualitatively different dynamics, are due to various distinct mechanisms. So far, bifurcation induced, noise- induced, shock-induced or rate-induced transitions have been studied extensively. In complex systems like the climate system or ecosystems, particularly in coupled versions of them, the dynamics of different components or different subsystems is characterized by different timescales. One simple example are ecosystems exhibiting allometric slowing down, that means that the duration of lifecycles increases with the trophic level. Coupling different compartments of the climate system involves also different timescales as the intrinsic timescales of flow patterns in the atmosphere are much faster than in the ocean. To study the dynamics of such systems requires the use of the methodology of slow-fast systems to account properly for such timescale separation. We will discuss the concept of critical manifolds in slow-fast sy...