Physics Commons^™

Enhanced Study Of Complex Systems By Unveiling Hidden Symmetries With Dynamical Visibility, Nhat Vu Minh Nguyen

2022 Symposium

One of the great challenges in complex and chaotic dynamics is to reveal its deterministic structures. These temporal dynamical structures are sometimes a consequence of hidden symmetries. Detecting and understanding them can allow the study of complex systems even without knowing the full underlying mathematical description of the system. Here we introduce a new technique, called Dynamical Visibility, that quantifies temporal correlations of the dynamics based upon some symmetry conditions. This visibility measures the departure of the dynamics from internal symmetries. We apply this technique to well-known chaotic systems, such as the logistic map and the circle map, as well …