2022/12/30 by Yu-Ting Chen, Yong Li, Chen, Yuting +1
Economics, Econometrics and Finance · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2212.14564
openalex publication_date 2022/12/30 · openalex created_date 2023/02/12 · openalex updated_date 2026/07/28
Whether there is similarity between two physical processes in the movement of objects and the complexity of behavior is an essential problem in science. How to seek similarity through the adoption of quantitative and qualitative research techniques still remains an urgent challenge we face. To this end, the concepts of similarity transformation matrix and similarity degree are innovatively introduced to describe similarity of orbits between two complicated discrete dynamical systems that seem to be irrelevant. Furthermore, we present a general optimal principle, giving a strict characterization from the perspective of dynamical systems combined with optimization theory. For well-known examples of chaotic dynamical systems, such as Lorenz attractor, Chua's circuit, R\rmossler attractor, Chen attractor, L\rmu attractor and hybrid system, with using of the homotopy idea, some numerical simulation results demonstrate that similarity can be found in rich characteristics and complex behaviors of chaotic dynamics via the optimal principle we presented.