Posted by: Dirk | October 5, 2010

Complex systems: Foreseeing tipping points

Marten Scheffer recently wrote about complex systems and tipping points in complex systems in Nature:

On page 456 of this issue, Drake and Griffen1 show that subtle changes in the pattern of fluctuations in a population can indicate whether that population is close to extinction. This is a step forward for conservation biology, but the wider implications are even more profound. The symptoms detected belong to a family of generic leading indicators that may help to determine whether a complex system is on the brink of collapse.

The new approaches for probing the vicinity of a tipping point are based on the idea that, whereas the equilibrium state reveals little at all, non-equilibrium dynamics should change in universal ways in the vicinity of tipping points. Thus, rather than looking at the state itself, we may have to look at its fluctuations if we want to know how vulnerable a system is.

This, to many, will be the search for the holy grail (or, Black Swan). Mathematical models are bad at predicting tipping points, and in financial markets the potential payoff to such a model would be in the billions of whatever currency you like. One interesting point is that the volatility goes up before the “crash” (the extinction of zooplankton in this case). That means that predicting the “crash” is possible – a result which is not undisputed, as many economists comfort themselves that nobody could have predicted the crisis and explained those that did away by pointing at chance: they were just lucky.

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