Interactive anisotropic walks in two dimensions generated from a three-state opinion dynamics model

Area of Science:

• Statistical Physics
• Complex Systems
• Agent-Based Modeling

Background:

• Interacting walker systems are typically studied in 1D virtual spaces.
• Opinion dynamics models often simplify agent interactions and spatial dimensions.

Purpose of the Study:

• To investigate a 2D interacting walker system governed by a 3-state opinion dynamics model.
• To analyze the impact of noise on phase transitions and distribution properties.

Main Methods:

• Simulating a 2D walker system with dynamics based on a fully connected three-state opinion model.
• Varying a noise parameter to drive continuous phase transitions.
• Analyzing scaling properties and probability distributions along X and Y axes.

Main Results:

• Identified three distinct regions based on the noise parameter.
• Observed non-conventional scaling properties and distributions in the absence of noise.
• Characterized bivariate and marginal distributions as modified biased Gaussian below the critical point and Gaussian above it.
• Extracted marginal probability distributions and scaling forms exhibiting power-law behavior.

Conclusions:

• The noise parameter is crucial for continuous phase transitions in this 2D opinion dynamics walker model.
• The system exhibits unique statistical properties, deviating from conventional forms, especially without noise.
• The directed nature of the walk significantly influences marginal distributions and observed scaling exponents.