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分散式分数标准地图:里曼-利乌维尔和卡普托
J A Méndez-Bermúdez1,2, R Aguilar-Sánchez3,4
1Instituto de Física, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico.
Chaos (Woodbury, N.Y.)
|February 3, 2025
概括
分数标准地图中的分散导致平均作用的指数式衰减. 平均平方的动作.
科学领域:
- 非线性动力学是一种非线性动力学.
- 分数微积分的计算.
- 混沌理论 混沌理论
背景情况:
- 现实的动态系统表现出固有的消散.
- 分数动力学提供了一个框架来模拟带有内存的系统.
- 分数标准地图 (fSM) 是具有内存的非线性地图.
研究的目的:
- 为了研究散射对分数标准地图的影响.
- 分析消散性fSM中平均动作和平均平方动作的行为.
- 为了比较分数顺序和散射强度对混乱轨道的影响.
主要方法:
- 被认为是里曼-利乌维尔 (RL) 和卡普托 (C) 分数标准图的消散版本.
- 专注于强烈混乱的轨道 (K≫1).
- 分析了平均动作 (In) 和平均平方动作 (In2) 作为非线性 (K),分数顺序 (α) 和散射强度 (γ) 的函数.
主要成果:
- 在两个消散性fSM中,证明了K的平均作用的指数衰减 (In≈I0exp(-γn))
- 表明In2RL-fSM在很大程度上独立于α,除了当α→1.
- 观察到任何α<2显著影响In2C-fSM的行为.
- 导出了In2RL-fSM(K,α,γ) 的分析表达式.
结论:
- 分散在分数动态系统的长期行为中起着至关重要的作用.
- 分数顺序α对平均平方的作用有不同的影响,这取决于分数导数的类型 (RL与C).
- 开发了分析工具来描述消散式分数地图的动态.
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