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基克的一般分数罗伦兹型方程:精确的解决方案和多维的离散地图
1Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia.
Entropy (Basel, Switzerland)
|November 26, 2025
概括
本研究介绍了使用一般分数导数和周期性的一般化洛伦兹式方程. 准确的分析解决方案和带有内存的离散地图是为这些复杂的混乱系统衍生出来的.
科学领域:
- 非线性动力学和混沌理论
- 分数微积分的计算.
- 数学物理 数学物理
背景情况:
- 洛伦兹型系统是分散动态系统中混乱行为的基本模型.
- 现有的模型往往缺乏描述具有记忆效应的系统的能力.
- 一般分数导数 (GFD) 提供了一个框架,用于将内存函数纳入动态系统.
研究的目的:
- 通过整合一般分数导数 (GFD) 和周期性来概括洛伦兹型方程.
- 为这些通用系统推导出精确的分析解决方案,适应非线性和内存.
- 开发具有内存 (DMM) 的离散地图,准确地表示被的GF Lorenz型系统的动态.
主要方法:
- 将一般分数导数 (GFD) 应用于洛伦兹式方程的应用.
- 用GFD和内存函数推导非线性方程的精确分析解.
- 从没有近似的精确解决方案构建具有内存 (DMM) 的多维离散地图.
主要成果:
- 准确的分析解决方案得到了广泛的非线性洛伦兹式方程与GFDs类别.
- 导出了具有记忆力的新型离散地图 (DMM),准确地描述了离散时间点的动态.
- 该方法允许对任意维度和复杂非线性产生DMM.
结论:
- 这项研究成功地使用GFD将洛伦兹型系统概括为GFD,使得能够对具有内存的系统进行建模.
- 由此产生的精确分析解决方案和DMM为分析复杂的混乱动态提供了强大的工具.
- 这项工作在理解和解决分数顺序混乱系统方面取得了重大进展.
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