Anticipating Critical Transitions
Egbert van Nes2012, Science
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Abstract
All ChangeResearch on early warning signals for critical transitions in complex systems such as ecosystems, climate, and global finance systems recently has been gathering pace. At the same time, studies on complex networks are starting to reveal which architecture may cause systems to be vulnerable to systemic collapse.Schefferet al.(p.344) review how previously isolated lines of work can be connected, conclude that many critical transitions (such as escape from the poverty trap) can have positive outcomes, and highlight how the new approaches to sensing fragility can help to detect both risks and opportunities for desired change.
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Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called 'early warning signals', and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.
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Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts [1, 2]. Because these transitions are often detrimental, the development of early warning signals is recognized as a major challenge [3]. Recent progress [4, 5, 6] builds on a mathematical framework in which the real-world system at hand is described by a low-dimensional equation system that captures the dynamics in terms of a small number of key variables. In this framework the critical transition often corresponds to a bifurcation. Here we show that in highdimensional systems, containing many variables, we frequently encounter an additional non-bifurcative mechanism that can lead to critical transitions. We develop a simple and intuitive early warning sign and illustrate both, mechanism and warning sign, in a range of examples, including network models of epidemics [7] and cooperation [8] and epidemiological data [9, 10]. This work thus establishes a connection between critical transitions and network science and provides an early warning sign for a new type of critical transition that could be relevant for many real world systems. In particular, in the light of the perspective to move to more complex models and utilize big data sources it can be anticipated that this new type of transition will be encountered frequently in the future.
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