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Updated: Jun 12, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

Hierarchical cluster structures in a one-dimensional swarm oscillator model.

Masatomo Iwasa1, Kazuki Iida, Dan Tanaka

  • 1Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japan. miwasa@r.phys.nagoya-u.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2010
PubMed
Summary

Interacting motile elements in a swarm oscillator model form hierarchical cluster patterns. This study mathematically derives stable configurations, revealing nested structures in one-dimensional space.

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Last Updated: Jun 12, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

Area of Science:

  • Physics
  • Complex Systems
  • Mathematical Modeling

Background:

  • Swarm intelligence and pattern formation are key areas in complex systems.
  • The Tanaka swarm oscillator model describes interacting motile elements forming dynamic patterns.
  • Understanding stable configurations is crucial for predicting emergent behavior.

Purpose of the Study:

  • To investigate cluster patterns in a one-dimensional swarm oscillator model.
  • To mathematically derive all static and stable configurations for a specific parameter set.
  • To analyze the structure of these stable final states.

Main Methods:

  • Mathematical derivation of static configurations.
  • Introduction of a renormalized expression for the swarm oscillator model.
  • Analysis of parameter space to identify stable states.

Main Results:

  • Identification of hierarchical cluster structures as the dominant stable final states.
  • Demonstration that clusters are composed of smaller, nested clusters.
  • Complete derivation of all static and stable configurations for the studied parameters.

Conclusions:

  • The swarm oscillator model exhibits complex, hierarchical self-organization.
  • Nested cluster structures represent a fundamental stable state in this one-dimensional system.
  • The renormalized model provides a powerful tool for analyzing such complex systems.