Lyapunov function method for the analysis of dissipative autonomous dynamic processes

A A Shestakov O V Druzhinina

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Lyapunov function method for the analysis of dissipative autonomous dynamic processes

机译：耗散自主动力过程分析的李雅普诺夫函数法

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We suggest a general technique for studying dissipative autonomous dynamic processes with the use of three types of special Lyapunov functions. We obtain sufficient conditions for the dissipativity of an autonomous dynamic process on a compact Euclidean space. The results can be used in the qualitative analysis of systems of population dynamics and chemical kinetics. [PUBLICATION ABSTRACT]

机译：我们建议使用三种特殊的Lyapunov函数来研究耗散自主动力过程的通用技术。我们为紧凑的欧几里得空间上的自主动力过程的耗散性提供了充分的条件。该结果可用于种群动力学和化学动力学系统的定性分析。 [出版物摘要]

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《Differential Equations》 |2009年第8期|p.1-9|共9页
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A A Shestakov O V Druzhinina;
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1. Lyapunov Function Method for the Analysis of Dissipative Autonomous Dynamic Processes [J] . Shestakov AA, Druzhinina OV Differential equations: A translation of differensial'nye uraveniya . 2009,第8期

机译：耗散自主动力过程分析的李雅普诺夫函数法
2. Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions [J] . Nosov V., Meda-Campana J. A., Gomez-Mancilla J. C., Mathematical Problems in Engineering . 2015,第Pta20期

机译：基于非传统Lyapunov函数的自治动态切换系统的稳定性分析
3. Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions [J] . V.Nosov, J. A.Meda-Campa?a, J. C.Gomez-Mancilla, Mathematical Problems in Engineering: Theory, Methods and Applications . 2015,第2期

机译：基于非传统Lyapunov函数的自治动力切换系统的稳定性分析
4. Extended Dissipativity Analysis of Delayed Memristive Neural Networks Based on A Parameter-Dependent Lyapunov Functional [C] . Chengda Lu, Xian-Ming Zhang, Min Wu, Australian and New Zealand Control Conference . 2018

机译：基于参数依赖的Lyapunov函数的时滞忆阻神经网络的扩展耗散性分析
5. Parameter-dependent Lyapunov functions and stability analysis of linear parameter-dependent dynamical systems. [D] . Zhang, Xiping. 2003

机译：依赖参数的Lyapunov函数和线性依赖参数的动力系统的稳定性分析。
6. EEG Analysis in Structural Focal Epilepsy Using the Methods of Nonlinear Dynamics (Lyapunov Exponents Lempel–Ziv Complexity and Multiscale Entropy) [O] . Tatiana V. Yakovleva, Ilya E. Kutepov, Antonina Yu Karas, 2020

机译：使用非线性动力学方法（Lyapunov指数Lempel-Ziv复杂度和多尺度熵）对结构性局灶性癫痫进行脑电图分析
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）

Lyapunov function method for the analysis of dissipative autonomous dynamic processes

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