通过非正态放大的几何复合通向混沌的新路径
A New Route to Chaos through the Geometric Composition of Non-Normal Amplification
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中文总结 AI 辅助
本文发现混沌出现的新路径取决于非正态切映射的时间顺序，并利用有序乘积增长率揭示混沌涌现尺度，提出通过微小相位作用实现全局混沌控制的新方法。
中文摘要 AI 辅助
当拉伸通过再注入被反复循环利用时，混沌便会出现。我们揭示了一条通向混沌的新路径，其中决定性的变量是非正态切映射的时间顺序：周期态和混沌态可以共享本质上相同的一步拉伸统计，而其有序乘积却获得相反的Lyapunov增长。我们引入了有序乘积增长率$h_L$，它定义在$L$个连续切映射之上，揭示了在一步中不可区分的状态如何在几何复合下分离，并确定了混沌出现时的有限复合尺度。我们利用这一机制建立了一种新的全局混沌控制形式：微小的相位作用重新定向连续的非正态放大方向，使其几何复合变为收缩，从而在固定耗散下抑制混沌，而无需减少局部放大或瞄准预先选定的轨道。
英文摘要
Chaos emerges when stretching is repeatedly recycled by reinjection. We uncover a new route to chaos in which the decisive variable is the temporal order of non-normal tangent maps: periodic and chaotic states can share essentially the same one-step stretching statistics while their ordered products acquire opposite Lyapunov growth. We introduce the ordered-product growth rate $h_L$ over $L$ successive tangent maps, which reveals how states indistinguishable at one step separate under geometric composition and identifies the finite composition scale at which chaos emerges. We use this mechanism to establish a new form of global chaos control: minute phase actions reorient the successive non-normal amplification directions so that their geometric composition becomes contracting, suppressing chaos at fixed dissipation without reducing local amplification or targeting a preselected orbit.
发表机构
- Institute of Risk Analysis, Prediction and Management (Risks-X), Southern University of Science and Technology（南方科技大学风险预测与管理研究所）
机构由 AI 辅助整理，请以论文原文为准。
