Critical phase transition in bee movement dynamics can be modeled using a two-dimensional cellular automaton.

Area of Science:

• Collective animal behavior
• Statistical physics
• Insect collective dynamics

Background:

• Animal collective behavior, including insects, often exhibits scale-free properties characteristic of critical phase transitions.
• Previous studies identified long-range spatial and temporal correlations in honeybee activity.
• Honeybee hive activity has been shown to display characteristics of a jamming process.

Purpose of the Study:

• To present a discrete model simulating honeybee collective behavior.
• To replicate key observed phenomena such as correlation length divergence and scale-free jammed clusters.
• To investigate the relationship between correlation length and the control parameter (density).

Main Methods:

• Development of a discrete model for simulating insect collective behavior.
• Analysis of real honeybee activity data.
• Comparison of model outputs with empirical data, focusing on correlation length and cluster distributions.

Main Results:

• The discrete model successfully replicates the divergence of correlation length with increasing density.
• The model reproduces the scale-free distribution of jammed clusters observed in honeybee behavior.
• A clear dependence of correlation length on density is demonstrated for both real data and the model.

Conclusions:

• The developed discrete model provides valuable insights into the critical dynamics of insect collective behavior.
• The model's ability to replicate jamming phenomena and scale-free distributions deepens our understanding of honeybee colony organization.
• This work bridges statistical physics concepts with empirical observations of insect societies.