TY - JOUR
T1 - Finding Similarity of Orbits Between Two Discrete Dynamical Systems via Optimal Principle
AU - Chen , Yuting
AU - Li , Yong
JO - Communications in Computational Physics
VL - 2
SP - 521
EP - 546
PY - 2025
DA - 2025/02
SN - 37
DO - http://doi.org/10.4208/cicp.OA-2022-0318
UR - https://global-sci.org/intro/article_detail/cicp/23872.html
KW - Similarity, optimal principle, homotopy, discrete dynamical system, chaotic attractor.
AB - <p style="text-align: justify;">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.</p>