Dr. Andres Aragoneses
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 as to experimental data from a diode laser with optical feedback and external modulation. Our results show the robustness of the method in characterizing dynamics and highlighting transitions in the dynamical behavior of a complex system. We envision that this can be a useful tool in experimental data, as it can extract key features of the deterministic laws that govern the dynamics of a system, despite the lack of knowledge of those specific quantitative descriptions.
Nguyen, Nhat Vu Minh, "Enhanced study of complex systems by unveiling hidden symmetries with Dynamical Visibility" (2022). 2022 Symposium. 8.
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