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Lorenz Attractors: Exploring its properties and the application value of chaos theories
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Abstract
Since Lorenz published Deterministic Nonperiodic Flow in 1963, Lorenz attractors and their equations have occupied an important position in the fields of mathematics, physics, meteorology and so on. Lorenz attractors reveal the aperiodic behavior and sensitivity to initial conditions in deterministic systems, which have attracted great attention in the scientific community. This paper deeply analyzes its characteristics, formation mechanism and performance in chaotic systems, and shows that it produces aperiodic behavior patterns in deterministic systems and is extremely sensitive to small changes in initial conditions, providing a new perspective for understanding the complexity and diversity of nature. Lorenz attractors are widely used in chaos theory, providing tools for chaos research and ideas for solving practical problems. It has shown its application potential in the field of meteorological prediction. It is expected to stimulate researchers’ interest in Lorenz attractors and chaos phenomena, promote the in-depth application and development of chaos theory in more fields, continue to reveal the mysteries of nature, and lead a new chapter in scientific exploration.
Keywords
Lorenz Attractor, chaos, Nonlinear dynamic system
[1]. Oestreicher, Christian. (2007) “A history of chaos theory.” Dialogues in clinical neuroscience, 9.3: 279-289.
[2]. Shen, Bo-Wen, et al. (2021) “Is weather chaotic? Coexistence of chaos and order within a generalized lorenz model.” Bulletin of the American Meteorological Society,102.1: E148-E158.
[3]. Tyutyunnik, Vyacheslav M. (2022) “Physical modelling of Earth’s climate: 2021 Nobel Prize winners in Physics Syukuro Manabe and Klaus Hasselmann.” Journal of Physics 11.
[4]. Ovsyannikov, I. I., and D. V. Turaev. (2016) “Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model.” Nonlinearity, 30.1: 115.
[5]. Tucker, Warwick. (1999) “The Lorenz attractor exists.” Comptes Rendus de l’Académie des Sciences-Series I-Mathematics, 328.12 : 1197-1202.
[6]. Lorenz, Edward N. (1963) “Deterministic nonperiodic flow.” Journal of atmospheric sciences, 20.2: 130-141.
[7]. Williams, Robert F. (1979) “The structure of Lorenz attractors.” Publications Mathematiques de l’IHES, 50: 73-99.
[8]. Munmuangsaen, Buncha, and Banlue Srisuchinwong. (2018) “A hidden chaotic attractor in the classical Lorenz system.” Chaos, Solitons & Fractals, 107: 61-66.
[9]. Ilyichev, V. Yu. (2021) “Development of a program for Lorenz attractor research and its use.” The Complex Systems, 1: 58-64.
Cite this article
Si,H. (2024). Lorenz Attractors: Exploring its properties and the application value of chaos theories. Theoretical and Natural Science,38,190-195.
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The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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Volume title: Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation
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