Memory-Driven Bounded Confidence Opinion Dynamics: A Hegselmann-Krause Model Based on Fractional-Order Methods

TL;DR

This paper introduces a fractional-order bounded confidence opinion dynamics model incorporating memory effects, enhancing the realism of opinion evolution modeling with proven convergence and consensus properties.

Contribution

It develops a novel fractional-order model based on the Hegselmann-Krause framework that captures persistent memory effects in opinion dynamics.

Findings

Model maintains convergence and consensus properties.

Addresses limitations of classical models like monotonicity.

Provides a more realistic representation of opinion evolution.

Abstract

Memory effects play a crucial role in social interactions and decision-making processes. This paper proposes a novel fractional-order bounded confidence opinion dynamics model to characterize the memory effects in system states. Building upon the Hegselmann-Krause framework and fractional-order difference, a comprehensive model is established that captures the persistent influence of historical information. Through rigorous theoretical analysis, the fundamental properties including convergence and consensus is investigated. The results demonstrate that the proposed model not only maintains favorable convergence and consensus characteristics compared to classical opinion dynamics, but also addresses limitations such as the monotonicity of bounded opinions. This enables a more realistic representation of opinion evolution in real-world scenarios. The findings of this study provide new insights and methodological approaches for understanding opinion formation and evolution, offering both theoretical significance and practical applications.