在修改复杂的Shimizu-Morioka系统中的过度吸引器上
Vyacheslav Kruglov1, Igor Sataev1
1Kotelnikov's Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russia.
Chaos (Woodbury, N.Y.)
|June 12, 2023
概括
研究人员修改了一个复杂值的石家庄-莫里奥卡系统,创建了一个均的过度引力吸引器. 这种新的系统,与原来的洛伦兹吸引器不同,表现出独特的膨胀和收缩特性,展示了新的动态系统行为.
科学领域:
- 动态系统 动态系统
- 混沌理论 混沌理论
- 非线性动力学是一种非线性动力学.
背景情况:
- 石家庄-莫里奥卡系统以其复杂的动力学和洛伦兹型吸引力而闻名.
- 均的超标吸引器是理解混乱系统的基础,其特点是指数级膨胀和收缩率.
- 之前的研究集中在具有真正洛伦兹吸引子的系统上,留下了探索修改系统的空间.
研究的目的:
- 介绍和分析一个修改的复杂值的Shimizu-Morioka系统.
- 调查修改系统中的吸引子的性质,特别是寻找均的过度波动.
- 为了比较修改系统的动态与原始的石家庄-莫里奥卡系统和斯梅尔-威廉姆斯电磁管.
主要方法:
- 修改复杂值的石家庄-莫里奥卡系统的数值模拟.
- 在Poincaré截面中分析吸引力的行为.
- 对流动及其Poincaré地图的触点子空间的横向性的数值验证.
主要成果:
- 修改后的系统呈现出一个均的超标吸引力,与原来的洛伦兹型吸引力不同.
- 吸引器在角方向显著膨胀,在横向方向强烈收缩,类似于斯梅尔-威廉姆斯电磁管.
- 数值测试证实了触点子空间的横向性,这是均过度波吸引器的一个关键特征.
- 在修改后的系统中没有观察到真正的洛伦兹型吸引子.
结论:
- 修改复杂值的石家庄-莫里奥卡系统提供了从具有真实洛伦兹吸引子的系统中衍生出的具有均超标吸引子的系统的第一个例子.
- 观察到的动力学,以膨胀和收缩为特征,与均的超标系统的特性保持一致.
- 这项研究为探索改造的混乱系统及其独特的吸引力结构开辟了新的途径.
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