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End date: 2023 × Start date: 2023 × DDC: 530 × Has files: Yes × WGL Institute: PIK ×

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Now showing 1 - 4 of 4
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    Complex systems in the spotlight: next steps after the 2021 Nobel Prize in Physics
    (Bristol : IOP Publ., 2023) Bianconi, Ginestra; Arenas, Alex; Biamonte, Jacob; Carr, Lincoln D; Kahng, Byungnam; Kertesz, Janos; Kurths, Jürgen; Lü, Linyuan; Masoller, Cristina; Motter, Adilson E; Perc, Matjaž; Radicchi, Filippo; Ramaswamy, Ramakrishna; Rodrigues, Francisco A; Sales-Pardo, Marta; San Miguel, Maxi; Thurner, Stefan; Yasseri, Taha
    The 2021 Nobel Prize in Physics recognized the fundamental role of complex systems in the natural sciences. In order to celebrate this milestone, this editorial presents the point of view of the editorial board of JPhys Complexity on the achievements, challenges, and future prospects of the field. To distinguish the voice and the opinion of each editor, this editorial consists of a series of editor perspectives and reflections on few selected themes. A comprehensive and multi-faceted view of the field of complexity science emerges. We hope and trust that this open discussion will be of inspiration for future research on complex systems.
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    Trends in recurrence analysis of dynamical systems
    (Les Ulis : EDP Sciences, 2023) Marwan, Norbert; Kraemer, K. Hauke
    The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot-based data analysis and to widen its application potential. We will give a brief overview about important and innovative developments, such as computational improvements, alternative recurrence definitions (event-like, multiscale, heterogeneous, and spatio-temporal recurrences) and ideas for parameter selection, theoretical considerations of recurrence quantification measures, new recurrence quantifiers (e.g. for transition detection and causality detection), and correction schemes. New perspectives have recently been opened by combining recurrence plots with machine learning. We finally show open questions and perspectives for futures directions of methodical research.
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    Path integral solutions for n-dimensional stochastic differential equations under α-stable Lévy excitation
    (College Park, Md : [Verlag nicht ermittelbar], 2023) Zan, Wanrong; Xu, Yong; Kurths, Jürgen
    In this paper, the path integral solutions for a general n-dimensional stochastic differential equations (SDEs) with α-stable Lévy noise are derived and verified. Firstly, the governing equations for the solutions of n-dimensional SDEs under the excitation of α-stable Lévy noise are obtained through the characteristic function of stochastic processes. Then, the short-time transition probability density function of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski (CKS) equation and the characteristic function, and its correctness is demonstrated by proving that it satisfies the governing equation of the solution of the SDE, which is also called the Fokker-Planck-Kolmogorov equation. Besides, illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method, and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.
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    Special Issue “Trends in recurrence analysis of dynamical systems”
    (Berlin ; Heidelberg : Springer, 2023) Marwan, Norbert; Webber, Charles L.; Rysak, Andrzej
    [No abstract available]