From the Amazon rainforest to human body cells: Quantifying stability

Jan 06, 2013

The Amazon rainforest, energy grids, and cells in the human body share a troublesome property: They possess multiple stable states. When the world's largest tropical forest suddenly starts retreating in a warming climate, energy supply blacks out, or cells turn carcinogenic, complex-systems science understands this as a transition between two such states. These transitions are obviously unwanted.

As they typically result from severe external perturbations, it is of vital interest how stable the most desirable state is. Surprisingly, this basic question has so far received little attention. Now scientists of the Potsdam Institute for Climate Impact Research (PIK), in a paper published in , propose a new concept for quantifying stability.

"Up to now, science was able to say if a complex system is stable or not, but it wasn't able to properly say how stable it is," says Peter J. Menck, lead author of the paper. The proposed concept is the first to fill this gap. "We conceive a system's alternative states as points in a with steep rocks and deep valleys," explains Menck. "In the sinks between the peaks, a system comes to rest like a rolling ball would. Now the likelihood that the system returns to a specific sink after suffering a severe blow strongly depends on how big the surrounding valley is." In the high-dimensional systems Menck and his colleagues study, the equivalent of the valley is called the basin of attraction. The basin's volume is the measure the authors suggest to use for the quantification of stability.

Getting the actual data still is a challenge

The authors envision the new concept to become a powerful tool for studies, including the assessment of climatic tipping elements like the . Under unabated global warming, this ecosystem might change from its present fertile forest state to a much drier savanna state. Such a transition would destroy one of the planet's most important CO2 sinks, thus contributing to further climate change. "Amazonian bistability arises from a positive feedback: Deep-rooting trees take up water and transpire it to the atmosphere" Menck says. Forest cover in the region increases overall rainfall and thereby improves its own growing conditions. If the forest cover gets pushed below a certain threshold, this mechanism doesn't work any more – the rainforest would die.

The "basin stability concept" is apt for quantifying this risk. However, it is critical to actually do this from measured data. "Other researchers recently have collected the characteristics in terms of precipitation, temperature, soil of rainforests and savannas under defined climatological conditions," Menck says. Still, the assessment is extremely challenging as the tipping of a forest is a rare event, so observation data is scarce. In contrast, observation data of human cells changing from a healthy state to cancer can be abundant. "So medical researchers told us that our concept could be quite helpful in better assessing the risk of sane cells to turning sick when disturbed by specific exogenous factors."

"Simple yet compelling – that's the way fundamental physics looks like"

Power grids have to function in good synchronization to assure that lights can be switched on everywhere anytime. Previous theory suggested that this should most easily be achieved if power grids had what researchers call a random structure, which in fact would yield many short-cuts between distant nodes. Yet in reality, grids look far more regular. Applying the basin stability concept shows why that is: In more regular grids, the desired synchronous state possesses a far bigger 'basin', hence is much more stable against .

"The basin 's applicability to high-dimensional systems allowed us to solve a puzzle that has long haunted complex network science," says Jürgen Kurths, a co-author of the paper and co-chair of PIK's research domain 'Transdisciplinary concepts and methods'. "Our new nonlinear approach jumps from a local to a whole system analysis, thus complementing previous research mostly based on linearization. This new concept is simple, yet compelling – that's the way fundamental physics looks like."

Explore further: Electric vehicles could stabilize large disturbances in power grid

More information: Menck, P.J., Heitzig, J., Marwan, N., Kurths, J. (2013): How basin stability complements the linear-stability paradigm. Nature Physics (advance online publication) doi:10.1038/NPHYS2516

Related Stories

Deforestation reduces rainfall in Africa

Sep 19, 2011

Deforestation in the rainforests of West Africa reduces rainfall over the rest of the forest, according to new University of Leeds research published in Geophysical Research Letters.

Amazon conservation policy working in Brazil (w/Video)

Jun 16, 2009

Contrary to common belief, Brazil's policy of protecting portions of the Amazonian forest from development is capable of buffering the Amazon from climate change, according to a new study led by Michigan State University ...

Forest and savanna can switch quickly

Oct 14, 2011

(PhysOrg.com) -- Two recent studies have found that environmental changes can bring previously stable forests and grasslands to tipping points that produce sudden large-scale and sometimes irreversible changes ...

New study examines effects of drought in the Amazon

Aug 02, 2010

Recent research surrounding the impact of drought in the Amazon has provided contradictory findings as to how tropical forests react to a drier and warmer climate. A new study published in the August 2 Early Edition of the ...

Recommended for you

Ultra-short X-ray pulses explore the nano world

6 hours ago

Ultra-short and extremely strong X-ray flashes, as produced by free-electron lasers, are opening the door to a hitherto unknown world. Scientists are using these flashes to take "snapshots" of the geometry ...

Measuring NIF's enormous shocks

11 hours ago

NIF experiments generate enormous pressures—many millions of atmospheres—in a short time: just a few billionths of a second. When a pressure source of this type is applied to any material, the pressure ...

User comments : 1

Adjust slider to filter visible comments by rank

Display comments: newest first

BishopBalderdash
1 / 5 (2) Jan 06, 2013
All of this was already worked out by Rene Thom.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.