THREE CONDITIONS LYAPUNOV EXPONENTS SHOULD SATISFY

机译：三个条件的LYAPUNOV指数应满足

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In contrast to the unilateral claim in some papers that a positive Lyapunov exponent means chaos, it was claimed in this paper that this is just one of the three conditions that Lyapunov exponent should satisfy in a dissipative dynamical system when the chaotic motion appears. The other two conditions, any continuous dynamical system without a fixed point has at least one zero exponent, and any dissipative dynamical system has at least one negative exponent and the sum of all of the 1-dimensional Lyapunov exponents id negative, are also discussed. In order to verify the conclusion, a MATLAB scheme was developed for the computation of the 1-dimensional and 3-dimensional Lyapunov exponents of the Duffing system with square and cubic nonlinearity.

机译：与某些论文中单方面声称正Lyapunov指数意味着混沌相反，本文声称这只是当混沌运动出现时，Lyapunov指数在耗散动力系统中应满足的三个条件之一。其他两个条件，任何不具有固定点的连续动力系统至少具有一个零指数，任何耗散动力系统至少具有一个负指数，并且所有一维Lyapunov指数的总和为负。为了验证该结论，开发了一种MATLAB方案，用于计算具有方形和三次非线性的Duffing系统的一维和三维Lyapunov指数。

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《19th Biennial Conference on Mechanical Vibration and Noise》|2003年|p.1611-1614|共4页
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作者
Lou Jingjun; Zhu Shijian;
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正文语种
中图分类一般工业技术;
关键词
lyapunov exponent; chaos; three conditions; duffing system;

机译：lyapunov指数;混沌;三个条件;达芬系统;

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1. Lyapunov Exponents and Moment Lyapunov Exponents of a Two-Dimensional Near-Nilpotent System [J] . W.-C. Xie Journal of Applied Mechanics: Transactions of the ASME . 2001,第3期

机译：二维近零幂系统的Lyapunov指数和矩Lyapunov指数
2. Lyapunov exponents, dual Lyapunov exponents, and multifractal analysis [J] . Aihua Fan, Yunping Jiang Chaos . 1999,第4期

机译：Lyapunov指数，双重Lyapunov指数和多重分形分析
3. Application of Backward Nonlinear Local Lyapunov Exponent Method to Assessing the Relative Impacts of Initial Condition and Model Errors on Local Backward Predictability [J] . Xuan LI, Jie FENG, Ruiqiang DING, 大气科学进展（英文版） . 2021,第009期

机译：Application of Backward Nonlinear Local Lyapunov Exponent Method to Assessing the Relative Impacts of Initial Condition and Model Errors on Local Backward Predictability
4. THREE CONDITIONS LYAPUNOV EXPONENTS SHOULD SATISFY [C] . Lou Jingjun, Zhu Shijian, American Society of Mechanical Engineers, Biennial Conference on Mechanical Vibration and Noise . 2003

机译：三个条件Lyapunov指数应该满足
5. Standardizing the Calculation of the Lyapunov Exponent for Human Gait Using Inertial Measurement Units [D] . Smith, Victoria Ann. 2019

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6. A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks [O] . Bulcsú Sándor, Bence Schneider, Zsolt I. Lázár, 2021

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7. Lyapunov Exponents: A Tool to Explore Complex DynamicsLyapunov Exponents: A Tool to Explore Complex Dynamics, Arkady Pikovsky and Antonio Politi, Cambridge U. Press, 2016, 295 p, $84.99, ISBN 978-1-107-03042-8 [O] . Robert C. Hilborn 2017

机译：Lyapunov指数：探索复杂Dynamicslyapunov指数的工具：探索复杂动态的工具，Arkady Pikovsky和Antonio Politi，Cambridge U.按，2016,295 P，$ 84.99，ISBN 978-1-107-03042-8

THREE CONDITIONS LYAPUNOV EXPONENTS SHOULD SATISFY

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