在无尺度网络上对多数投票模型的滴滴有限尺寸缩放
D S M Alencar1, T F A Alves1, F W S Lima1
1Departamento de Física, Universidade Federal do Piauí, 57072-970 Teresina - PI, Brazil.
Physical review. E
|August 16, 2023
概括
在无规模网络上的多数投票模型表现出非普遍的关键行为,指数取决于网络连接. 一个新的有限大小理论解释了这些行为和缩放关系.
科学领域:
- 统计物理 统计物理
- 网络科学 网络科学
- 复杂的系统复杂的系统.
背景情况:
- 多数投票模型是研究共识形成的关键工具.
- 以前的研究表明,在某些网络上,这个模型中的非普遍的关键行为.
- 网络结构,特别是无尺度属性的关键指数上的作用尚未完全理解.
研究的目的:
- 在无尺度网络上研究多数投票模型的关键行为.
- 开发一个有限大小理论来解释观察到的非普遍的临界指数.
- 将缩放关系泛化并通过模拟验证它们.
主要方法:
- 在无关联网络上开发一个有限大小理论用于多数投票模型.
- 对由外部场 (媒体影响) 和网络切断影响的大小依赖的分析.
- 蒙特卡洛模拟用于验证理论预测和缩放关系.
主要成果:
- 临界指数是非普遍的,并且取决于 5/2 < γ < 7/2.2. 的度分布指数 (γ).
- 对于 γ ≥ 7/2,该模型属于与埃尔多斯-雷尼随机图相同的普遍性类.
- 对关键行为进行逻辑校正,特别是在 γ = 7/2.2 时观察到.
结论:
- 有限大小理论成功地解释了在无尺度网络上的多数投票模型的非普遍关键行为.
- 网络结构显著影响共识形成动态和关键现象.
- 该研究提供了一个统一的框架,用于理解不同网络类型的多数投票模型.
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