在非马科维亚人群动态中,从一个超稳定状态逃离
Ohad Vilk1,2,3, Michael Assaf1
1Racah Institute of Physics, <a href="https://ror.org/03qxff017">The Hebrew University of Jerusalem</a>, Jerusalem 91904, Israel.
Physical review. E
|November 20, 2024
概括
这项研究探讨了存储效应的随机模型中的长期动态. 强大的内存可以创建新的稳定状态,而无限的平均等待时间则会导致可比式系统中不同的缩放行为.
科学领域:
- 理论物理 理论物理
- 随机过程 随机过程
- 数学生物学 数学生物学
背景情况:
- 非马科夫模型捕获系统与内存,偏离标准的马科夫假设.
- 脂肪尾等待时间分布在反应动态中引入了长期记忆效应.
- 了解长期的行为对于生物和物理系统至关重要.
研究的目的:
- 调查非指数等待时间的单个人群随机模型的长期动态.
- 分析记忆诱导状态和扩展模式的出现.
- 开发非马科夫系统的理论框架.
主要方法:
- 在非马科夫系统中使用温泽尔-克拉默斯-布里卢恩 (Wentzel-Kramers-Brillouin,简称WKB) 方法.
- 分析了具有有限和无限平均等待时间分布的系统.
- 检查的原型例子:基因切换,人口建立和灭绝.
主要成果:
- 在有限平均值的状态下,一个由记忆诱导的 (元) 稳定状态可以与强大的记忆出现.
- 获得了平均种群大小和逃生时间的明确结果.
- 在无限平均状态下,二位式系统表现出两种不同的缩放状态,分开很长时间.
结论:
- 非马科夫效应,特别是长期记忆,显著改变系统动态.
- 系统的行为严重取决于等待时间分布的属性 (有限与无限平均值).
- 开发的WKB方法为分析复杂的非马科夫现象提供了强大的工具.
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