Biswas-Chatterjee-Sen kinetic exchange opinion model for two connected groups

TL;DR

This paper analyzes a kinetic opinion model with two groups, revealing a new antisymmetric ordered state and its stability conditions, confirmed by simulations, advancing understanding of opinion dynamics in modular social structures.

Contribution

Introduces and analyzes a new antisymmetric ordered state in the Biswas-Chatterjee-Sen opinion model with modular interactions, extending prior knowledge of possible system states.

Findings

Discovery of a stable antisymmetric ordered state.

Identification of thresholds for stability related to interaction strength and noise.

Numerical simulations confirm analytical predictions.

Abstract

We consider a kinetic model of opinion dynamics known as the Biswas-Chatterjee-Sen model with a modular interaction structure. The system consists of two groups of agents that feature more frequent interactions within each group and rarer interactions between agents of different groups. We use the mean-field analytical approximation to determine that aside from previously known ordered and disordered states, a new antisymmetric ordered state is stable, where each group has an opposite dominant opinion. The limits of system interaction strength and noise for the stability of such a state are determined, with a discontinuous transition from an antisymmetric to a symmetric state happening if thresholds are exceeded. The results of numerical agent-based simulations confirm our analytical predictions and show that the critical values of noise and interaction strength are predicted with good accuracy.