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Fractional core-based collapse mechanism and structural optimization in complex systems

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Abstract

Catastrophic and major disasters in real-world systems ranging from financial markets and ecosystems, often show generic early-warning signals that may indicate a collapse. Hence, understanding the collapse mechanism of a complex network and predicting its process are of uttermost importance. However, these challenges are often hindered by the extremely high dimensionality of the underlying system. We present here the concept of the fractional core (F-core) that considers the contribution of the network topology and dynamics to systematically analyze the collapse process in such networks, and encompass a broad range of dynamical systems, from mutualistic ecosystems to regulatory dynamics. We offer testable predictions on the tipping point, and, in particular, prove that the extinction of the maximum F-core of a network is an efficient indicator of whether a system completely collapses. The results show that the death of species or cells in a low-order F-core may improve the average density and have little influence on the tipping point. Generally, the principle of the F-core demonstrates how complex systems collapse and opens an innovative optimization strategy to uncover the optimal structure of systems.

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 72171193, 72231008, 72071153), Key Research and Development Program of Shaanxi Province (Grant No. 2022KW-15), and Natural Science Foundation of Shaanxi Province (Grant No. 2023-JC-QN-0802).

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Author notes

  1. Si S B and Lv C C have the same contribution to this work.

Authors and Affiliations

  1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, China

    Shubin Si, Zhiqiang Cai & Zhen Wang

  2. Key Laboratory of Industrial Engineering and Intelligent Manufacturing (Ministry of Industry and Information Technology), Xi’an, 710072, China

    Shubin Si & Zhiqiang Cai

  3. School of Information and Control Engineering, Xi’an University of Architecture and Technology, Xi’an, 710072, China

    Changchun Lv & Dongli Duan

  4. Instiute of Physics, Humboldt-University, Berlin, 10099, Germany

    Jurgen Kurths

  5. Potsdam Institute for Climate Impact Research, Potsdam, 14473, Germany

    Jurgen Kurths

Authors
  1. Shubin Si
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  2. Changchun Lv
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  3. Zhiqiang Cai
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  4. Dongli Duan
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  6. Zhen Wang
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Corresponding authors

Correspondence to Dongli Duan or Zhen Wang.

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Appendixes A and B. The Appendix includes experimental setup and results. The supporting information is available online at info.scichina.com and link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.

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Si, S., Lv, C., Cai, Z. et al. Fractional core-based collapse mechanism and structural optimization in complex systems. Sci. China Inf. Sci. 66, 192202 (2023). https://doi.org/10.1007/s11432-022-3731-x

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  • DOI: https://doi.org/10.1007/s11432-022-3731-x

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