Cyclic opinion dynamics with adaptive confidence and expressed-private opinion duality

School of Physical Science and Technology, Beijing University of Posts and Telecommunications Beijing 100876, PRC

Received: 26 August 2025
Accepted: 25 November 2025

Abstract

Contemporary societies exhibit increasing opinion polarization and fragmentation, driven by complex interactions between private beliefs and publicly expressed views. This study introduces a novel framework for cyclic opinion dynamics on a circle, integrating three key mechanisms: 1) a Kuramoto-inspired circular opinion space capturing cyclical preference shifts, 2) adaptive interaction strength where influence decays nonlinearly with opinion differences (replacing static bounded confidence), and 3) explicit duality between private convictions (ϕ) and public expressions (θ). We propose two models: Model A with static private opinions reveals how the relative social influence strength and confidence kernel sharpness (α) interact to drive transitions between incoherence, fragmentation, and multi-cluster consensus. Model B incorporates co-evolving private opinions with relaxation time τ, demonstrating that final cluster number depends solely on α and τ but not λ as private beliefs gradually align with expressed opinions. Crucially, slower alignment preserves early fragmentation seeded by initial opinion diversity.