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No Access Submitted: 17 December 2019 Accepted: 02 April 2020 Published Online: 24 April 2020

How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales featured

Chaos 30, 043129 (2020); https://doi.org/10.1063/1.5142827
Nico Wunderling1,2,3,a), Benedikt Stumpf1,4, Jonathan Krönke1,2, Arie Staal5, Obbe A. Tuinenburg5,6, Ricarda Winkelmann1,2, and Jonathan F. Donges1,5
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ABSTRACT
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.

ACKNOWLEDGMENTS

This work has been carried out within the framework of the PIK FutureLab on Earth Resilience in the Anthropocene. N.W. and R.W. acknowledge the financial support of the IRTG 1740/TRP 2015/50122-0 project funded by Deutsche Forschungsgemeinschaft (DFG) and FAPESP. N.W. is grateful for a scholarship from the Studienstiftung des deutschen Volkes. A.S. and J.F.D. acknowledge support from the European Research Council project Earth Resilience in the Anthropocene (No. 743080 ERA). A.S. and O.A.T. acknowledge support from the Bolin Centre for Climate Research. O.A.T. acknowledges funding from the Netherlands Organization for Scientific Research Innovational Research Incentive Schemes VENI (No. 016.171.019). J.F.D. is grateful for financial support by the Stordalen Foundation via the Planetary Boundary Research Network (PB.net) and the Earth League’s EarthDoc program. The authors acknowledge financial support from the Leibniz Association (Project DominoES). The authors gratefully acknowledge the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research, and the Land Brandenburg for supporting this project by providing resources on the high performance computer system at the Potsdam Institute for Climate Impact Research. The authors also gratefully acknowledge discussions with Ann-Kristin Klose, Marc Wiedermann, and Jobst Heitzig. The authors declare no competing financial interest. The data that were used in this study are available from the corresponding author upon reasonable request.

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  1. © 2020 Author(s). Published under license by AIP Publishing.

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