Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

Area of Science:

• Complex systems
• Collective behavior modeling
• Statistical physics

Background:

• The two-dimensional optimal velocity (2d-OV) model simulates systems with asymmetric interactions.
• This model is applicable to pedestrian dynamics and collective motion of organisms.

Purpose of the Study:

• To investigate pattern formation in the 2d-OV model within a maze-like corridor.
• To analyze the stability of these emergent patterns using the Wasserstein metric.

Main Methods:

• Simulated particle behavior in a 2d-OV model maze.
• Applied the Wasserstein metric to quantify pattern stability.
• Mapped patterns into Wasserstein metric space for analysis.

Main Results:

• Particles formed optimal patterns within the maze.
• Pattern stability was found to be sensitive to model parameters.
• Two distinct, stable macroscopic patterns were identified and observed consistently.

Conclusions:

• The 2d-OV model exhibits stable pattern formation in confined environments.
• Model sensitivity is a key factor influencing pattern stability.
• The emergence of regular, cohesive macroscopic patterns is confirmed.