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Related Concept Videos

Causes of Similarity-Dissimilarity Effect01:26

Causes of Similarity-Dissimilarity Effect

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Related Experiment Video

Updated: Jul 15, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
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Temporal self-similarity reveals percolation universality classes in complex networks.

Sheng Fang1, Jun Meng2, Qing Lin1

  • 1School of Systems Science, Beijing Normal University, Beijing, China.

Nature Communications
|July 13, 2026
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Complex systems exhibit temporal self-similarity in fragmentation dynamics. Two critical exponents characterize universality classes, revealing distinct real-world network behaviors from idealized models.

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Area of Science:

  • Complex systems science
  • Statistical physics
  • Network science

Background:

  • Catastrophic fragmentation and structural transitions are common in complex systems.
  • Universality classes governing these dynamics are often unclear due to heterogeneity and lack of clear thresholds.

Purpose of the Study:

  • To discover a universal phenomenon governing dynamic percolation across complex networks.
  • To establish a framework for characterizing universality classes and critical exponents in heterogeneous systems.

Main Methods:

  • Tracking statistics of incremental growth events in dynamic percolation.
  • Identifying and analyzing Fisher-type critical exponents (τc and τs).
  • Developing scaling relations to derive other critical exponents.

Main Results:

  • Discovered temporal self-similarity in dynamic percolation across diverse networks.
  • Fragmentation dynamics are governed by two independent critical exponents, τc and τs.
  • Real-world networks (biological, social, infrastructural) show distinct universality classes compared to idealized models.

Conclusions:

  • Established a dynamic paradigm bridging statistical physics and real-world resilience.
  • Developed a parameter-free, scalable approach to classify structural vulnerabilities in heterogeneous systems.
  • Highlighted the impact of higher-order structural features on network dynamics.