2014/01/31 by Christian Kuehn, Gerd Zschaler, Thilo Gross · 1 citation
Physics and Astronomy · Mathematics · Biochemistry, Genetics and Molecular Biology · #nlin.AO #math.DS #q-bio.QM
paper · pdf · doi:10.1038/srep13190
published as Scientific Reports, Vol. 5, 13190, 2015 · revised version
arxiv created 2015/01/08 · arxiv updated 2017/02/28
Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress builds on a mathematical framework in which a real-world system is described by a low-dimensional equation system with a small number of key variables, where the critical transition often corresponds to a bifurcation. Here we show that in high-dimensional systems, containing many variables, we frequently encounter an additional non-bifurcative saddle-type mechanism leading to critical transitions. This generic class of transitions has been missed in the search for early-warnings up to now. In fact, the saddle-type mechanism also applies to low-dimensional systems with saddle-dynamics. Near a saddle a system moves slowly and the state may be perceived as stable over substantial time periods. We develop an early warning sign for the saddle-type transition. We illustrate our results in two network models and epidemiological data. This work thus establishes a connection from critical transitions to networks and an early warning sign for a new type of critical transition. In complex models and big data we anticipate that saddle-transitions will be encountered frequently in the future.