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准自行车的门穿越时间理论与对大脑节律的应用
Mathias Roman1, Ivan L'Heureux1, Arthur Powanwe1
1Department of Physics, <a href="https://ror.org/03c4mmv16">University of Ottawa</a>, Ottawa, Ontario, Canada K1N 6N5.
Physical review. E
|November 20, 2024
概括
这项研究分析了物理和生物系统中的随机幅度波动. 我们发现,到达值的首次返回时间 (FRT) 是由单个参数控制的,并表现出指数级的行为,为神经动力学提供了洞察力.
科学领域:
- 物理 物理学 物理
- 神经科学是一个神经科学.
- 随机过程 随机过程
背景情况:
- 两维奥恩斯坦-乌伦贝克彩色噪声过程的振幅遵循一维雷利过程,模拟半循环中的随机振幅波动.
- 这些半循环是噪音诱导的振荡,围绕着一个平衡与复杂的固有值,在物理和生物系统中相关.
研究的目的:
- 为了研究时间间隔的概率密度 (第一次返回时间 - - FRT),使振幅保持在固定值以下或以上.
- 使用FRT统计数据来描述大脑节律功率外游 (爆发),雪崩和分支过程.
主要方法:
- 使用最近提出的技术,涉及福克-普朗克固有函数扩展和正常化校正,以解决非可规范化的FRT密度.
- 将FRT密度的分析表达式与Rayleigh过程在各种参数上的数值实现进行比较.
主要成果:
- 雷利工艺的分析FRT密度表达式与值以上和以下轨迹的数值模拟有很好的一致性.
- FRT是由一个单一的元参数 (Δ) 控制的,即噪声强度与线性稳定系数的比率.
- 平均FRT与值与sqrt[Δ]的比率是不变的,FRT密度随着时间的推移表现出指数式的行为.
结论:
- 该研究提供了关于准循环和随机威尔逊-考恩神经方程中的值跨越时间统计的见解.
- 确定这些跨越门的统计数据中没有严格的权力法缩放,揭示了由单个元参数支配的普遍性质.
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