In this study, we investigate how specific micro-interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erdős–Rényi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop, and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease in the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of a very high motif occurrence for each of the four investigated motifs, suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erdős–Rényi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole.
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April 2020
Research Article|
April 24 2020
How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales

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Nico Wunderling
;
Nico Wunderling
a)
1
Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association
, 14473 Potsdam, Germany
2
Institute of Physics and Astronomy, University of Potsdam
, 14476 Potsdam, Germany
3
Department of Physics, Humboldt University of Berlin
, 12489 Berlin, Germany
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Benedikt Stumpf
;
Benedikt Stumpf
1
Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association
, 14473 Potsdam, Germany
4
Department of Physics, Free University of Berlin
, 14195 Berlin, Germany
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Jonathan Krönke
;
Jonathan Krönke
1
Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association
, 14473 Potsdam, Germany
2
Institute of Physics and Astronomy, University of Potsdam
, 14476 Potsdam, Germany
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Arie Staal
;
Arie Staal
5
Stockholm Resilience Centre, Stockholm University
, Stockholm SE-10691, Sweden
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Obbe A. Tuinenburg
;
Obbe A. Tuinenburg
5
Stockholm Resilience Centre, Stockholm University
, Stockholm SE-10691, Sweden
6
Copernicus Institute, Faculty of Geosciences, Utrecht University
, 3584 CB Utrecht, The Netherlands
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Ricarda Winkelmann
;
Ricarda Winkelmann
1
Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association
, 14473 Potsdam, Germany
2
Institute of Physics and Astronomy, University of Potsdam
, 14476 Potsdam, Germany
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Jonathan F. Donges
Jonathan F. Donges
1
Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association
, 14473 Potsdam, Germany
5
Stockholm Resilience Centre, Stockholm University
, Stockholm SE-10691, Sweden
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Nico Wunderling
1,2,3,a)
Benedikt Stumpf
1,4
Jonathan Krönke
1,2
Arie Staal
5
Obbe A. Tuinenburg
5,6
Ricarda Winkelmann
1,2
Jonathan F. Donges
1,5
1
Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association
, 14473 Potsdam, Germany
2
Institute of Physics and Astronomy, University of Potsdam
, 14476 Potsdam, Germany
3
Department of Physics, Humboldt University of Berlin
, 12489 Berlin, Germany
4
Department of Physics, Free University of Berlin
, 14195 Berlin, Germany
5
Stockholm Resilience Centre, Stockholm University
, Stockholm SE-10691, Sweden
6
Copernicus Institute, Faculty of Geosciences, Utrecht University
, 3584 CB Utrecht, The Netherlands
a)
Author to whom correspondence should be addressed: [email protected]
Chaos 30, 043129 (2020)
Article history
Received:
December 17 2019
Accepted:
April 02 2020
Connected Content
A companion article has been published:
Microscale rainforest interactions can result in vulnerabilities across large regions
Citation
Nico Wunderling, Benedikt Stumpf, Jonathan Krönke, Arie Staal, Obbe A. Tuinenburg, Ricarda Winkelmann, Jonathan F. Donges; How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales. Chaos 1 April 2020; 30 (4): 043129. https://doi.org/10.1063/1.5142827
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