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在一个半周期驱动的断片直线振荡器中,双放牧两叉路口路线
Run Liu1, Celso Grebogi2, Yuan Yue1
1Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, China.
Chaos (Woodbury, N.Y.)
|June 23, 2023
概括
研究人员发现了一条新的途径,以奇怪的非混沌吸引器 (SNA) 在一个片式线性振荡器. 这种双放牧的分叉将半周期性轮转化为SNA,其属性经过分析和数值验证.
科学领域:
- 非线性动力学是一种非线性动力学.
- 混沌理论 混沌理论
- 双分支线理论 双分支线理论
背景情况:
- 断片线性振荡器在半周期性激发下表现出复杂的动态.
- 在非线性系统中,理解过渡到混乱和奇怪的非混乱吸引子 (SNA) 是至关重要的.
研究的目的:
- 通过双放牧分叉,研究从准周期性圆到奇怪的非混乱吸引器 (SNA) 的路径.
- 通过分析来确定这个分叉的最大位移.
- 为了描述由此产生的SNAs的特性.
主要方法:
- 一个带有近周期激发的线性振荡器的分析.
- 在双放牧分叉过程中最大位移的分析表达式的导出.
- 使用利亚普诺夫指数,相位灵敏度,功率光谱和碎形结构对SNA属性的数值验证.
主要成果:
- 确定了双放牧分叉作为从半周期性体到SNA的途径.
- 证明,随着准周期圆柱失去光滑并变得不可差异化,SNAs会出现.
- 通过利亚普诺夫指数证实了SNA的非混乱性质,并通过光谱和碎形分析证实了它们的奇特特征.
- 在各种参数间隔观察到SNA,包括一个显著的范围,不会导致准周期或混乱轨道.
结论:
- 双放牧分叉为SNAs提供了一条新的路线,在片式线性振荡器中.
- SNAs可以表现为各种参数模式,提供对其发生的更广泛的理解.
- 该研究在分析和数值上描述了SNAs的过渡和属性,为非线性动力学研究做出了贡献.
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