连续时间随机在网络上行走.
Sarvesh K Upadhyay1, R K Singh2,3
1Banaras Hindu University, Department of Physics, Varanasi 221005, India.
Physical review. E
|August 19, 2025
概括
网络上的连续时间随机步行显示了独立于等待时间分布的稳定状态. 然而,放松动态和访问节点的数量取决于等待时间指数,显示出不同的缩放行为.
科学领域:
- 复杂的系统复杂的系统.
- 网络科学 网络科学
- 统计物理 统计物理
背景情况:
- 连续时间随机步行 (CTRWs) 是网络上运输现象的基本模型.
- 了解等待时间分布对CTRW动态的影响对于各种应用至关重要.
研究的目的:
- 调查等待时间分布如何影响网络上的CTRW的稳定状态,放松和探索动态.
- 描述复发时间分布和不同访问节点的平均数量对等待时间属性的依赖.
主要方法:
- 在网络结构上分析各种等待时间分布 (ψ(τ)) 的CTRW.
- 基于网络拓和等待时间指数 (α) 的稳定状态属性和放松行为推导.
- 作为时间和网络参数的函数,计算访问的不同节点的平均数 (Si(t) .
主要成果:
- 稳态分布是独立于 ψ(τ) 的,并且仅依赖于局域网的社区.
- 放松动态和复发时间分布极为依赖等待时间分布的指数α.
- 对于α<1,不同访问节点的平均数量随着时间的推移在代数上增长 (Si(t) ∼t^α),而对于α>1,它表现出网络大小依赖的缩放.
结论:
- 等待时间的性质显著影响了CTRWs的过渡动态,但不是最终的稳定状态.
- CTRW在放松和探索时表现出不同的缩放行为,基于等待时间分布的尾部行为.
- 该研究提供了对异常运输现象和由CTRWs规范的网络探索策略的见解.
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