Acero Marcos, Lyons Sean, Aragoneses Andrés, Pattanayak Arjendu K
Department of Physics and Astronomy, Carleton College, Northfield, MN 55057, USA.
Department of Physics, Whitman College, Walla Walla, WA 99362, USA.
Entropy (Basel). 2024 Nov 12;26(11):969. doi: 10.3390/e26110969.
Identifying signs of regularity and uncovering dynamical symmetries in complex and chaotic systems is crucial both for practical applications and for enhancing our understanding of complex dynamics. Recent approaches have quantified temporal correlations in time series, revealing hidden, approximate dynamical symmetries that provide insight into the systems under study. In this paper, we explore universality patterns in the dynamics of chaotic maps using combinations of complexity quantifiers. We also apply a recently introduced technique that projects dynamical symmetries into a "symmetry space", providing an intuitive and visual depiction of these symmetries. Our approach unifies and extends previous results and, more importantly, offers a meaningful interpretation of universality by linking it with dynamical symmetries and their transitions.
识别复杂和混沌系统中的规律性迹象并揭示动力学对称性，对于实际应用以及增进我们对复杂动力学的理解都至关重要。最近的方法对时间序列中的时间相关性进行了量化，揭示了隐藏的、近似的动力学对称性，这些对称性为深入了解所研究的系统提供了线索。在本文中，我们使用复杂性量化指标的组合来探索混沌映射动力学中的普适模式。我们还应用了一种最近引入的技术，将动力学对称性投影到一个“对称空间”中，从而对这些对称性进行直观且可视化的描述。我们的方法统一并扩展了先前的结果，更重要的是，通过将普适性与动力学对称性及其转变联系起来，为普适性提供了有意义的解释。
