English
 
Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Complex networks of interacting stochastic tipping elements: Cooperativity of phase separation in the large-system limit

Authors
/persons/resource/kohler.jan

Kohler,  Jan
Potsdam Institute for Climate Impact Research;

/persons/resource/Nico.Wunderling

Wunderling,  Nico
Potsdam Institute for Climate Impact Research;

/persons/resource/Donges

Donges,  Jonathan Friedemann
Potsdam Institute for Climate Impact Research;

Vollmer,  Jürgen
External Organizations;

External Ressource
No external resources are shared
Fulltext (public)
There are no public fulltexts stored in PIKpublic
Supplementary Material (public)
There is no public supplementary material available
Citation

Kohler, J., Wunderling, N., Donges, J. F., Vollmer, J. (2021): Complex networks of interacting stochastic tipping elements: Cooperativity of phase separation in the large-system limit. - Physical Review E, 104, 4, 044301.
https://doi.org/10.1103/PhysRevE.104.044301


Cite as: https://publications.pik-potsdam.de/pubman/item/item_25957
Abstract
Tipping elements in the Earth System receive increased scientific attention over the recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element undergoes a drastic shift in its state upon an additional small parameter change when close to its tipping point. Recently, the focus of research broadened towards emergent behavior in networks of tipping elements, like global tipping cascades triggered by local perturbations. Here, we analyze the response to the perturbation of a single node in a system that initially resides in an unstable equilibrium. The evolution is described in terms of coupled nonlinear equations for the cumulants of the distribution of the elements. We show that drift terms acting on individual elements and offsets in the coupling strength are sub-dominant in the limit of large networks, and we derive an analytical prediction for the evolution of the expectation (i.e., the first cumulant). It behaves like a single aggregated tipping element characterized by a dimensionless parameter that accounts for the network size, its overall connectivity, and the average coupling strength. The resulting predictions are in excellent agreement with numerical data for Erd\"os-R\'enyi, Barab\'asi-Albert and Watts-Strogatz networks of different size and with different coupling parameters.