Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions

Area of Science:

• Complex Systems
• Statistical Physics
• Computational Modeling

Background:

• Agent-based models (ABMs) are complex to analyze at large scales.
• Dynamical networks of interacting particles present significant modeling challenges.
• Macroscopic models offer a simplified approach to understanding emergent behaviors.

Purpose of the Study:

• To numerically investigate a macroscopic model derived from an agent-based model.
• To validate the macroscopic model's predictions against microscopic simulations.
• To assess the model's consistency and utility for large-scale dynamical network analysis.

Main Methods:

• Numerical simulations of a macroscopic aggregation-diffusion equation.
• Comparison of stationary states and phase transitions in 1D and 2D systems.
• Validation against theoretical criteria for phase transitions and bifurcation types.

Main Results:

• Macroscopic model accurately predicts phase transitions and bifurcation types in 1D.
• Numerical simulations in 2D show excellent agreement with theoretical predictions.
• The macroscopic model consistently approximates the underlying particle dynamics.

Conclusions:

• The macroscopic model provides a validated and consistent approximation of microscopic particle dynamics.
• This model is a powerful tool for large-scale modeling of systems with dynamical networks.
• The study partially validates the derivation of the macroscopic model from its microscopic origins.