2023/10/05 by Xiaoying Wang, Yong Li, Wang, Xiaoying +3
Engineering · Mathematics · Physics and Astronomy · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2310.03383
openalex publication_date 2023/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.