标题： 无偏网络上置信区间动力学中的非单调共识转变 显示英文标题

标题： Nonmonotonic consensus transitions in bounded-confidence dynamics on unbiased networks

摘要： 我们研究了在通过威尔逊算法生成的稀疏、无偏网络上的赫格塞曼-克劳斯意见动态模型，揭示了网络连通性和置信范围如何共同决定集体行为。 通过系统地探索由置信水平$\epsilon$和平均度密度$\mu$所构成的参数空间，我们构建了全面的相图，将出现的稳态分类为不同程度的碎片化和共识。 我们发现了一种非单调的重新进入转变，其中增加的连通性可能会悖论性地抑制共识，并表明由于结构隔离，在低连通性下完全一致是无法实现的。 收敛时间表现出两种不同的减速：在$\epsilon \sim 1/N$附近的有限尺寸、依赖于连通性的共振，以及与已建立的碎片化到共识转变相关的临界峰值。 虽然临界置信阈值$\epsilon_c$在大系统规模下稳定在 0.2 左右，但有限尺寸效应和稀疏连通性在较小群体中显著改变了动力学和相边界。 我们的结果为网络拓扑与意见动态之间的相互作用提供了新的见解，并指出了增加连通性可能阻碍而非促进共识的条件。 显示英文摘要

摘要： We study the Hegselmann-Krause model of opinion dynamics on sparse, unbiased networks generated via Wilson's algorithm, unveiling how network connectivity and confidence bounds jointly determine collective behavior. By systematically exploring the parameter space spanned by the confidence level $\epsilon$ and the mean degree density $\mu$, we construct comprehensive phase diagrams that classify the emergent steady states into different degrees of fragmentation and consensus. We uncover a nonmonotonic re-entrant transition where increased connectivity can paradoxically suppress consensus, and show that full unanimity is unattainable at low connectivity due to structural isolation. Convergence times exhibit two distinct slowdowns: a finite-size, connectivity-dependent resonance near $\epsilon \sim 1/N$, and a critical peak associated with the established fragmentation-to-consensus transition. While the critical confidence threshold $\epsilon_c$ stabilizes near 0.2 for large system sizes, finite-size effects and sparse connectivity significantly alter the dynamics and phase boundaries in smaller populations. Our results offer new insights into the interplay between network topology and opinion dynamics, and highlight conditions under which increased connectivity may hinder, rather than promote, consensus.