集体反转多数规则动力学中的交互规模与异议容忍度
Interaction size and dissent tolerance in majority-rule dynamics with collective reversal
中文总结 AI 辅助
该研究提出含异议容忍度$d$的多数规则集体反转模型，通过平均场分析与模拟揭示其相结构变化，发现激活选择性可调控集体有序性等动力学特征。
中文摘要 AI 辅助
我们提出一种多数规则模型，其中即使只有少数成员持异议，高度一致的群体也可触发集体反转。异议容忍度$d$通过让近乎一致的群体组成具备反转资格，扩展了严格一致动力学。平均场分析与模拟显示，这一改变在性质上改变了相结构：严格一致下，仅当$n=3$和$n=4$时存在物理可及的相变；允许异议则恢复了更大交互规模下的相变，将固定的交互规模阈值替换为$(n,d)$平面内的可及性边界。当激活窗口足够宽时，方向不对称性可通过鞍结分岔消除两个有序吸引子之一，产生单一稳定集体状态。在单侧情形下，提高异议容忍度可缩短达成共识的暂态过程，但不改变其对种群规模的对数依赖关系。激活选择性是调控集体有序性、双稳态及共识动力学的独立控制参数。
英文摘要
We introduce a majority-rule model in which collective reversal can be activated in highly aligned groups even when a limited number of members dissent. The dissent tolerance $d$ extends the strict-unanimity dynamics by making near-unanimous group compositions eligible for reversal. Mean-field analysis and simulations reveal that this change qualitatively alters the phase structure. Under strict unanimity, a physically accessible transition exists only for $n=3$ and $n=4$. Allowing dissent restores transitions at larger interaction sizes, replacing the fixed interaction-size threshold with an accessibility boundary in the $(n,d)$ plane. When the activation window is sufficiently broad, directional asymmetry can eliminate one of the two ordered attractors through a saddle-node bifurcation, producing a single stable collective state. In the one-sided case, increasing the dissent tolerance can shorten the transient approach to consensus but leaves its leading logarithmic dependence on population size unchanged. Activation selectivity acts as an independent control parameter for collective ordering, bistability, and consensus dynamics.
