不平滑的折叠作为临界点.
1School of Mathematical and Computational Sciences, Massey University, Palmerston North 4410, New Zealand.
Chaos (Woodbury, N.Y.)
|February 5, 2025
概括
动态系统中不平滑的折叠会导致解决方案发生碰撞并消失. 我们的研究表明,简化模型在这种分叉后往往缺乏稳定状态,导致系统行为不可预测.
科学领域:
- 动态系统理论 动态系统理论
- 两分支线分析分析
- 没有平滑的机械.
背景情况:
- 当解决方案与开关分流体相互作用时,非平滑的动态系统表现出复杂的行为.
- 不平滑的折叠,以溶液的消灭为特征,在这些系统中代表了一个关键的现象.
研究的目的:
- 研究非平滑折叠对动态系统中有限不变集合存在的影响.
- 分析这种分叉后的简化模型 (截断系统) 的行为.
主要方法:
- 在菲利普洛夫系统,混合系统和连续的零碎平滑普通微分方程中对边界平衡分叉的数学分析.
- 使用连续的断片式线性地图检查放牧类型事件.
- 用一个具体的例子演示,以说明局部不变集合的缺失.
主要成果:
- 经历非平滑折叠的系统的领先顺序截断通常缺乏除分叉之外的边界不变集合.
- 这种不变集的缺失被证明是各种类别的不平滑系统和放牧事件.
- 高阶项不太可能恢复局部不变集合,这表明系统动态发生了根本性的变化.
结论:
- 不平滑的折叠可以破坏系统的稳定,导致吸引力转移到新的状态.
- 这些发现提供了对截断不平滑动态系统中观察到的全球分叉结构的见解.
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