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Piecewise linear model of self-organized hierarchy formation
Tomoshige Miyaguchi1, Takamasa Miki1, Ryota Hamada1
1Department of Mathematics, Naruto University of Education, Tokushima 772-8502, Japan.
Physical Review. E
|October 20, 2020
Summary
This study explores self-organized hierarchy formation using a simplified Bonabeau model. Researchers found stable two- and three-level hierarchies and analyzed agent behavior transitions.
Area of Science:
- Complex Systems
- Agent-Based Modeling
- Mathematical Biology
Background:
- The Bonabeau model describes self-organized hierarchy formation in social insects.
- Understanding the emergence and stability of hierarchical structures is crucial in various scientific domains.
Purpose of the Study:
- To investigate the Bonabeau model of self-organized hierarchy formation using a piecewise linear approximation.
- To analyze the existence and stability of hierarchical solutions and agent behavior transitions.
Main Methods:
- Simulations of a piecewise linear agent model.
- Mean-field approximation of the agent model for analytical insights.
- Analysis of bifurcations and stability of solutions.
Main Results:
- Identified two-level and three-level hierarchical solutions in simulations.
- Observed transitions from nonergodic to ergodic behaviors in agents.
- Analytically demonstrated asymmetric two-level solutions and coexisting stable/unstable three-level solutions.
- Showcased emergence of solutions via supercritical-pitchfork-like bifurcations.
Conclusions:
- The simplified Bonabeau model supports complex hierarchical structures.
- Agent behavior and solution stability are intricately linked.
- Analytical and simulation approaches provide complementary insights into self-organization.
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