title: Early warning signs for saddle-escape transitions in complex networks.
abstract: 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.
authors: Vienna University of Technology, 1040 Vienna, Austria.
authors: Christian
authors: C
authors: Kuehn
authors: TNG Technology Consulting, 85774 Unterföhring, Germany.
authors: Gerd
authors: G
authors: Zschaler
authors: University of Bristol, Merchant Venturers School of Engineering, BS8 1TR Bristol, UK.
authors: Thilo
authors: T
authors: Gross
mesh_terms: D005075:Biological Evolution; D003141:Communicable Diseases / Q000453:epidemiology; D004196:Disease Outbreaks / Q000706:statistics & numerical data; D004198:Disease Susceptibility / Q000453:epidemiology; D058872:Epidemics / Q000706:statistics & numerical data; D005716:Game Theory; D006801:Humans; D008457:Measles / Q000453:epidemiology; D008954:Models, Biological; D006113:United Kingdom / Q000453:epidemiology