Complex systems consist of parts that interact with each other in a non-trivial (non-linear) way, like coupled neurons in the brain, like spatially distributed interacting ecological species, or like the ice-ocean-atmosphere coupling in the climate system. Such systems are often very sensitive to perturbations as obvious in smoke patterns of a cigar, in turbulent patterns of a fluid, in the fibrillation state of the heart immediately before sudden cardiac death, or in spatially and temporally irregular (chaotic) chemical reactions. Some of these complex systems - very counterintuitively - can suddenly go extinct. This is like a smoke pattern suddenly disappearing, or an ecological species suddenly going extinct. If such drastic changes happen to a system, we usually look for an external influence - like a strong predator - that causes such a spontaneous system collapse. New research shows that some systems can drastically change their behavior without any external influence. Systems develop by themselves into a critical state from where they suddenly collapse. How can a system live for a long time, obey statistically asymptotic behavior, and then suddenly change its behavior without warning? This is like a billiard ball irregularly bouncing around on a frictionless table for many many months until the ball suddenly escapes through a tiny hole. Finding and quantifying such critical holes in a mathematical space is crucial to the understanding of sudden collapses in nature, like the instantaneous stop of a chemical reaction, the extinction of ecological species, or the understanding of projected drastic regime changes in the (Arctic) climate system. Currently it is mathematically not understood which systems undergo such collapses, i.e. which systems have such critical holes from where they can escape instantaneously into a new behavior. The images to the right depict simulations of four such systems (please click on them for more information). In all of these systems the time of the collapse is not predictable in advance of the collapse.
This research is based upon work supported by the National Science Foundation under grant number PHY-0653086, and by the Arctic Region Supercomputing Center at the University of Alaska Fairbanks as part of the Department of Defense High Performance Computing Modernization Program.
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