分数主方程中的人口异质性,集体自我强化和强烈的记忆效应
1Department of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom.
Physical review. E
|December 11, 2023
概括
这项研究为随机步行者引入了分数主方程,揭示了人口异质性如何通过记忆创造自我强化的步行. 这项研究将异质合唱团与随机步行中的强烈记忆效应联系起来.
科学领域:
- 统计物理 统计物理
- 随机过程 随机过程
背景情况:
- 随机步行是物理学和数学中的基本模型.
- 了解随机步行中的复杂行为,如记忆和自我强化,对于各种应用至关重要.
- 人口异质性可以显著改变随机过程的动态.
研究的目的:
- 为连续时间随机步行与异质群体制定一个分数主方程.
- 在随机步行中建立集合异质性和记忆效应之间的联系.
- 分析这些自我强化的随机走路的统计性质,包括方差和扩散.
主要方法:
- 制定一个包含随机过渡概率的分数主方程.
- 对人口异质性的分析导致有条件过渡概率 (自我强化).
- 用分数Poisson过程和离散的自我强化的随机步行来使用附属的集合平均解决方案的导出.
主要成果:
- 这项研究建立了异质合唱团和具有强烈记忆力的随机步行之间的联系.
- 分数主方程的整体平均解得到.
- 方差表现出超扩散,即使分数指数接近1.
结论:
- 分数主方程为建模复杂的随机步行动态提供了一个框架.
- 随机步行中的集体自我强化可以从人口异质性中出现.
- 这些发现表明,在具有记忆和异质性的系统中,超扩散行为.
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