两个动力系统之间的相似性
Similarity Between Two Dynamical Systems
AI总结：
本文围绕两个动力系统的相似性问题，通过同胚映射极小化子衡量相似程度，证明其存在的充要条件，结合Takens嵌入定理建立相似性定理，并经多系统仿真验证，拓展了动力系统共轭理论。
摘要：
本文的核心研究内容是探究两个动力系统之间的相似程度。类比经典的Hartman-Grobman定理，两个系统之间的关系可通过同胚映射$K$建立关联，核心是研究极小化子$K^*$以衡量相似程度。我们证明了极小化子$K^*$存在的充分条件与必要条件（最大值原理）。此外，我们基于Takens嵌入定理建立了相似性定理。作为应用，对Lorenz系统、Chua电路系统与Chen系统进行了仿真测试，结果阐释了相似性的内涵，拓展了动力系统中的共轭概念。
英文摘要：
The main focus of this paper is to explore how much similarity between two dynamical systems. Analogous to the classical Hartman-Grobman theorem, the relationship between two systems can be linked by a homeomorphic map $K$, and the core is to study the minimizer $K^*$ to measure the degree of similarity. We prove the sufficient conditions and necessary conditions (the maximum principle) for the existence of the minimizer $K^*$. Further, we establish similarity theorem based on the Takens embedding theorem. As applications, Lorenz system, Chua's circuit system and Chen's system are simulated and tested. The results illustrate what is the similarity, which extends the conjugacy in dynamical systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
