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      Predicting catastrophic shifts

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          Abstract

          Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes, such as desertification and coral reef collapses, which are considered as a prominent threat to sustainability and to the well-being of millions. Still, the methods proposed so far for the prediction of an imminent transition are quite ineffective, and some empirical and theoretical studies suggest that actual transitions may occur smoothly, without an abrupt shift. Here we present a new diagnostic tool, based on monitoring the dynamics of clusters through time. Our technique discriminates between systems with local positive feedback, where the transition is abrupt, and systems with negative density dependence, where the transition is smooth. Analyzing the spatial dynamics of these two generic scenarios, we show that changes in the critical cluster size provide a reliable early warning indicator for both transitions. Our method may allow for the prediction, and thus hopefully the prevention of such transitions, avoiding their destructive outcomes.

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          Most cited references10

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          Early warnings of regime shifts: a whole-ecosystem experiment.

          Catastrophic ecological regime shifts may be announced in advance by statistical early warning signals such as slowing return rates from perturbation and rising variance. The theoretical background for these indicators is rich, but real-world tests are rare, especially for whole ecosystems. We tested the hypothesis that these statistics would be early warning signals for an experimentally induced regime shift in an aquatic food web. We gradually added top predators to a lake over 3 years to destabilize its food web. An adjacent lake was monitored simultaneously as a reference ecosystem. Warning signals of a regime shift were evident in the manipulated lake during reorganization of the food web more than a year before the food web transition was complete, corroborating theory for leading indicators of ecological regime shifts.
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            Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States

            (2000)
            This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic nonequilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.
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              The Importance of Being Discrete (and Spatial)

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                Author and article information

                Journal
                2015-06-10
                Article
                1506.03344
                34c072f8-4778-4fae-bbff-d500bd487162

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                q-bio.PE cond-mat.stat-mech nlin.PS

                Condensed matter,Evolutionary Biology,Nonlinear & Complex systems
                Condensed matter, Evolutionary Biology, Nonlinear & Complex systems

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