探索扩散合在时间空间混乱中的作用
1Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA.
Chaos (Woodbury, N.Y.)
|October 7, 2024
概括
我们使用共变的利亚普诺夫向量 (CLVs) 在合地图中研究混乱动力学. 扩散强度的增加最初会导致周期性行为,然后再回到混乱状态,CLV显示空间结构的演变.
科学领域:
- 非线性动力学是一种非线性动力学.
- 统计物理学的统计物理.
- 复杂的系统复杂的系统.
背景情况:
- 扩展系统中的混乱动态对于理解复杂现象至关重要.
- 结合的地图格子 (CMLs) 提供了一个简化但强大的模型来研究时空混沌.
- 共变的利亚普诺夫向量 (CLVs) 提供了对混乱系统的几何和动态性质的洞察.
研究的目的:
- 为了研究扩散合强度对一个一维合地图格子的混乱动态的影响.
- 量化空间结构和利亚普诺夫光谱的演变作为扩散的函数.
- 分析CLV的空间特征及其与合操作员的关系.
主要方法:
- 利用一个一维格子的扩散式合的二次地图.
- 采用共变的利亚普诺夫向量 (CLV) 来分析混乱的动态.
- 使用合运算符的固有值分析计算了利亚普诺夫指数和分数维度.
- 量化了CLV的空间特征,并将它们与合运算符的自身向量进行了比较.
主要成果:
- 领先的利亚普诺夫指数从正数到零的快速下降,随着扩散强度的增加,创造了一个周期动态的窗口.
- 周期窗口之外的混乱动态显示了领先的利亚普诺夫指数的最小变化,除了最高的扩散强度.
- 作为扩散强度的函数,对利亚普诺夫光谱和碎形维度的分析描述得到了推导.
- 发现CLV是由物理模式组成的,主要的CLV随着合强度的增加而呈现下降的局部化.
- 违反Oseledets分裂主导地位表明邻近的CLV之间纠增加,扩散更强.
结论:
- 扩散合显著改变了CML的混乱动态,引入周期窗口并影响空间结构的形成.
- CLVs提供了一个强大的工具来表征在合的混乱系统中的时空行为和模式定位.
- 观察到的CLV纠表明,在强度合的混乱格子中,独立错误增长的分解.
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