Year: 2025
Author: Yuting Chen, Yong Li
Communications in Computational Physics, Vol. 37 (2025), Iss. 2 : pp. 521–546
Abstract
Whether there is a 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, to give 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, Rössler attractor, Chen attractor, Lü attractor and hybrid system, with using of the homotopy idea, some numerical simulation results reveal that a similarity can be found in rich characteristics and complex behaviors of chaotic dynamics via the optimal principle we presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0318
Communications in Computational Physics, Vol. 37 (2025), Iss. 2 : pp. 521–546
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Similarity optimal principle homotopy discrete dynamical system chaotic attractor.