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A single topological neighbor is enough to create order in multi-agent systems with non-local interactions. This study explores collective dynamics and information flow in 2D and 3D environments.

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Area of Science:

  • Complex systems
  • Network science
  • Topology

Background:

  • Collective dynamics are crucial in multi-agent systems.
  • Understanding order emergence in complex systems is a key challenge.
  • Discrete Ricci curvature offers a novel approach to analyze system interactions.

Purpose of the Study:

  • To investigate collective dynamics in 2D and 3D multi-agent systems.
  • To explore the role of discrete Ricci curvature in generating system order.
  • To analyze topological information flow and clustering dynamics.

Main Methods:

  • Generating 2D and 3D environments by minimizing discrete Ricci curvature.
  • Implementing local and non-local interaction neighborhoods.
  • Utilizing Hodge spectral entropy and mean Forman-Ricci curvature for analysis.

Main Results:

  • Significant system order emerges with even a single effective topological neighbor in non-local interaction systems.
  • Distinct topological information flow patterns were identified.
  • Clustering dynamics were quantitatively analyzed.

Conclusions:

  • The findings highlight the power of topological interactions in driving collective order.
  • Discrete Ricci curvature is a valuable tool for understanding multi-agent system dynamics.
  • The study provides insights into information flow and organization in complex systems.