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Networked dynamic systems with higher-order interactions: stability versus complexity.

Ye Wang1, Aming Li1,2, Long Wang1,2

  • 1Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China.

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Summary
This summary is machine-generated.

Complex systems stability is enhanced by higher-order interactions when modeled using set structures. A simple rule shows that fewer common sets between nodes stabilize these systems, contrary to previous complexity assumptions.

Keywords:
higher-order interactionnetworked systemset structurestability criteria

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Area of Science:

  • Complex Systems Science
  • Network Theory
  • Mathematical Biology

Background:

  • Complex systems stability is crucial but often limited by traditional network models that only capture pairwise interactions.
  • Higher-order interactions, involving more than two components, are essential for accurately describing many real-world systems.
  • Set structures offer a more comprehensive framework for modeling both pairwise and higher-order interactions.

Purpose of the Study:

  • To derive stability criteria for complex systems incorporating higher-order interactions using set structures.
  • To investigate the role of higher-order interactions in community stability within networked systems.
  • To challenge the conventional understanding that increased complexity (more interactions) inherently destabilizes systems.

Main Methods:

  • Development and application of stability criteria based on set structures for networked systems.
  • Mathematical analysis to determine the conditions under which higher-order interactions influence system stability.
  • Exploration of the relationship between the number of common sets and overall system stability.

Main Results:

  • A simple rule for stability: networked systems with set structures are stabilized if the expected number of common sets for any two nodes is less than one.
  • Higher-order interactions can stabilize complex systems, contrary to the notion that increased interactions lead to instability.
  • Formation of more local sets can enhance the stability of networked systems with higher-order interactions.

Conclusions:

  • Set structures provide a powerful tool for analyzing the stability of complex systems with higher-order interactions.
  • The findings reveal a nuanced role for complexity, demonstrating how higher-order interactions can promote stability under specific conditions.
  • The derived stability rule offers a new perspective on understanding and engineering robust complex systems.