在自然数中演变的离散动态系统家族的轨道
1Division of Control and Dynamical Systems, Instituto Potosino de Investigación Científica y Tecnológica, Camino a la Presa San José 2055, Col. Lomas 4ta. Sección, 78216 San Luis Potosí, SLP, México.
Chaos (Woodbury, N.Y.)
|January 3, 2025
概括
这项研究引入了一个新类型的单维离散动态系统. 这些系统表现出复杂的行为,包括固定点和周期周期,为数论和离散数学提供了洞察力.
科学领域:
- 离散数学是离散的数学.
- 动态系统理论 动态系统理论
- 数学理论是数的理论.
背景情况:
- 一维离散动态系统在模拟复杂现象方面是至关重要的.
- 了解具有状态空间N+ (正整数) 的系统的行为对于各种应用至关重要.
- 之前的研究已经探索了离散动态系统的各种方面,但具有参数定义进化规则的特定类需要进一步研究.
研究的目的:
- 定义和研究一种新型的一维离散动态系统类别.
- 分析这些系统的动态,特别关注定义部分内的整数演变.
- 在这些系统中识别和描述固定点和周期周期的存在.
主要方法:
- 该研究根据两个参数定义了一个系统类:影响进化规则的最近邻居数和自然数 Λ = {1, 2, ..., b} 的部分.
- 研究了特定的单维地图,其中一个整数的下一个状态是由其最近邻数的和减去b的倍数决定的.
- 引入了两个单参数地图家族,以分析它们在 Λ 段内的动态.
主要成果:
- 该研究确定了研究的动态系统中固定点和周期周期的共存.
- 分析了 Λ 段内引入的单参数地图家族的动态.
- 集合 Λ-b 中的数字的排序是通过这些家族建立的.
结论:
- 这篇论文成功地介绍和分析了一种新的一维离散动态系统类别.
- 这些发现表明,固定点和周期周期的出现,突出了这些系统的丰富动态.
- 该研究为进一步探索这些参数定义离散动态系统的特性和应用提供了基础.
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