Lyapunov exponents, dual Lyapunov exponents, and multifractal analysis

Aihua Fan; Yunping Jiang

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Lyapunov exponents, dual Lyapunov exponents, and multifractal analysis

机译：Lyapunov指数，双重Lyapunov指数和多重分形分析

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It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of one-dimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps.

机译：结果表明，与一维扩展折叠图的缩放函数有关的李雅普诺夫指数和对偶李雅普诺夫指数均具有多重分形性质。这以定量的方式揭示了由这些图确定的动力学的复杂性。

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《Chaos》 |1999年第4期|共5页
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Aihua Fan; Yunping Jiang;
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正文语种 eng
中图分类自然科学总论;
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1. 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
2. Multifractal analysis of the Lyapunov exponent for the backward continued fraction map [J] . Iommi G Ergodic Theory and Dynamical Systems . 2010,第Pta1期

机译：向后连续分数图的Lyapunov指数的多重分形分析
3. Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices [J] . De-Jun Feng Israel Journal of Mathematics . 2009,第1期

机译：矩阵乘积和多重分形分析的李雅普诺夫指数。第二部分：一般矩阵
4. Modified Lorentz and Chua Systems Largest Lyapunov Exponent and Statistical Characteristics Analysis [C] . K. M. Kafarov, S. S. Loginov, M. Yu. Zuev Systems of Signal Synchronization, Generating and Processing in Telecommunications Conference . 2021

机译：改进的Lorentz和Chua Systems最大的Lyapunov指数和统计特征分析
5. Balance control of constrained bipedal standing and stability analysis using the concept of Lyapunov exponents. [D] . Yang, Caixia. 2008

机译：使用Lyapunov指数的概念控制约束的两足动物站立和稳定性。
6. Analysis of Pseudo-Lyapunov Exponents of Solar Convection Using State-of-the-Art Observations [O] . Giorgio Viavattene, Mariarita Murabito, Salvatore L. Guglielmino, 2021

机译：利用最先进的观测分析太阳对流的伪Lyapunov指数
7. EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed TarekShahriar Abstract—An EMD-chaos based approach is proposed todiscriminate EEG signals corresponding to healthy persons,and epileptic patients during seizure-free intervals and seizureattacks. An electroencephalogram (EEG) is first empiricallydecomposed to intrinsic mode functions (IMFs). The nonlineardynamics of these IMFs are quantified in terms of the largestLyapunov exponent (LLE) and correlation dimension (CD).This chaotic analysis in EMD domain is applied to a large groupof EEG signals corresponding to healthy persons as well asepileptic patients (both with and without seizure attacks). It isshown that the values of the obtained LLE and CD exhibitfeatures by which EEG for seizure attacks can be clearlydistinguished from other EEG signals in the EMD domain.Thus, the proposed approach may aid researchers in developingeffective techniques to predict seizure activities. Index Terms—Electroencephalogram (EEG), empiricalmode decomposition (EMD), largest Lyapunov exponent (LLE),correlation dimension (CD), epileptic seizures. The Authors are with the Electrical and Electronic EngineeringDepartment, Bangladesh University of Engineering and Technology,Dhaka-1000, Bangladesh (e-mail: imamul@eee.buet.ac.bd) PDF Cite: S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed Tarek Shahriar, "EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain," International Journal of Computer and Electrical Engineering vol. 4, no. 3, pp. 326-330, 2012. PREVIOUS PAPER Perception of Emotions Using Constructive Learningthrough Speech NEXT PAPER Physical Layer Impairments Aware OVPN Connection Selection Mechanisms Copyright © 2008-2013. International Association of Computer Science and Information Technology Press (IACSIT Press) [O] . S. M. Shafiul Alam, Syed TarekShahriar 2012

机译：EEG信号在EMD域S. S. Shafiul Alam，S中的非线性动力学使用非线性动力学。 M. Shafiul Alam，Aurangozeb和Syed Tarekshahriar摘要 - 基于EMD Chaos的方法，提出了对应于健康人的EEG信号，癫痫发作期间的癫痫患者和Seizureattacks。脑电图（EEG）首先被凭经上分解为内在模式功能（IMF）。这些IMF的非线性动力学在最大范围的指数（LLE）和相关尺寸（CD）方面是量化的。本域中的混沌分析应用于与健康人相对应的大型脑电图（Asepileptic患者）（两者都有癫痫发作）。因此，所获得的LLE和CD表展的价值可以从EMD领域的其他EEG信号中清晰地区分脑电图的表达展示。本拟议的方法可以帮助研究人员以预测癫痫发作的癫痫发作技术。索引术语 - 脑电图（EEG），仿真态分解（EMD），最大的Lyapunov指数（LLE），相关维度（CD），癫痫发作。作者与电气电子和电子工程公司，孟加拉国工程和技术大学，孟加拉国达卡 - 1000（电子邮件：imamul@eee.buet.ac.bd）pdf cite：s. m. shafiul Alam，s。 M. Shafiul Alam，Aurangozeb和Syed Tarek Shahriar，“EEG信号歧视在EMD领域的非线性动态，”计算机电气工程卷国际杂志。 4，不。 3，pp。326-330,2012，上一篇论文对情绪的看法，使用建设性的学习言论下一篇论文物理层障碍意识到OVPN连接选择机制版权所有©2008-2013。国际计算机科学与信息技术协会出版社（IACSIT Press）
8. Finite-Time Lagrangian Transport Analysis: Stable and Unstable Manifolds of Hyperbolic Trajectories and Finite-Time Lyapunov Exponents [R] . Branicki, M., Wiggins, S. 2009

机译：有限时滞拉格朗日输运分析：双曲线轨迹和有限时间Lyapunov指数的稳定和不稳定流形

Lyapunov exponents, dual Lyapunov exponents, and multifractal analysis

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