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

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

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 Creators:
Kohler, Jan1, Author              
Wunderling, Nico1, Author              
Donges, Jonathan Friedemann1, Author              
Vollmer, Jürgen2, Author
Affiliations:
1Potsdam Institute for Climate Impact Research, ou_persistent13              
2External Organizations, ou_persistent22              

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Free keywords: Physics, Physics and Society, physics.soc-ph,Nonlinear Sciences, Chaotic Dynamics, nlin.CD
 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.

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 Dates: 2021-08-152021-09-152021-10-01
 Publication Status: Finally published
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: PIKDOMAIN: RD1 - Earth System Analysis
Organisational keyword: RD1 - Earth System Analysis
Organisational keyword: FutureLab - Earth Resilience in the Anthropocene
Research topic keyword: Complex Networks
Research topic keyword: Nonlinear Dynamics
Research topic keyword: Tipping Elements
Model / method: Open Source Software
Model / method: Nonlinear Data Analysis
MDB-ID: Entry suspended
DOI: 10.1103/PhysRevE.104.044301
 Degree: -

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Title: Physical Review E
Source Genre: Journal, SCI, Scopus, p3
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Pages: - Volume / Issue: 104 (4) Sequence Number: 044301 Start / End Page: - Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/150218
Publisher: American Physical Society (APS)