The Experts below are selected from a list of 52038 Experts worldwide ranked by ideXlab platform
Silvius Klein - One of the best experts on this subject based on the ideXlab platform.
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Lyapunov Exponents of linear cocycles continuity via large deviations
2016Co-Authors: Pedro Duarte, Silvius KleinAbstract:Introduction.- Estimates on Grassmann Manifolds.- Abstract Continuity of Lyapunov Exponents.- The Oseledets Filtration and Decomposition.- Large Deviations for Random Cocycles.- Large Deviations for Quasi-Periodic Cocycles.- Further Related Problems.
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positive Lyapunov Exponents for higher dimensional quasiperiodic cocycles
Communications in Mathematical Physics, 2014Co-Authors: Pedro Duarte, Silvius KleinAbstract:We consider an m-dimensional analytic cocycle \({\mathbb{T} \times \mathbb{R}^m \ni (x, \vec{\psi}) \mapsto (x + \omega, A (x) \cdot \vec{\psi}) \in \mathbb{T} \times \mathbb{R}^m}\), where \({\omega \notin \mathbb{Q}}\) and \({A \in C^\omega (\mathbb{T}, \mathrm{Mat}_m (\mathbb{R}))}\). Assuming that the d × d upper left corner block of A is typically large enough, we prove that the d largest Lyapunov Exponents associated with this cocycle are bounded away from zero. The result is uniform relative to certain measurements on the matrix blocks forming the cocycle. As an application of this result, we obtain nonperturbative (in the spirit of Sorets–Spencer theorem) positive lower bounds of the nonnegative Lyapunov Exponents for various models of band lattice Schrodinger operators.
N V Kuznetsov - One of the best experts on this subject based on the ideXlab platform.
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matlab code for Lyapunov Exponents of fractional order systems
International Journal of Bifurcation and Chaos, 2018Co-Authors: Mariusf Danca, N V KuznetsovAbstract:In this paper, the Benettin–Wolf algorithm to determine all Lyapunov Exponents for a class of fractional-order systems modeled by Caputo’s derivative and the corresponding Matlab code are presented...
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invariance of Lyapunov Exponents and Lyapunov dimension for regular and irregular linearizations
Nonlinear Dynamics, 2016Co-Authors: N V Kuznetsov, T A Alexeeva, G A LeonovAbstract:Nowadays the Lyapunov Exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic Exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov Exponents, LEs). In this work, the relation between Lyapunov Exponents and Lyapunov characteristic Exponents is discussed. The invariance of Lyapunov Exponents for regular and irregular linearizations under the change of coordinates is demonstrated.
Elif Derya Ibeyli - One of the best experts on this subject based on the ideXlab platform.
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Lyapunov Exponents probabilistic neural networks for analysis of eeg signals
Expert Systems With Applications, 2010Co-Authors: Elif Derya IbeyliAbstract:A new approach based on the implementation of probabilistic neural network (PNN) is presented for classification of electroencephalogram (EEG) signals. In practical applications of pattern recognition, there are often diverse features extracted from raw data which needs recognizing. Because of the importance of making the right decision, the present work is carried out for searching better classification procedures for the EEG signals. Decision making was performed in two stages: computation of Lyapunov Exponents as feature vectors and classification using the classifiers trained on the extracted features. The aim of the study is classification of the EEG signals by the combination of Lyapunov Exponents and the PNN. The purpose is to determine an optimum classification scheme for this problem and also to infer clues about the extracted features. The present research demonstrated that the Lyapunov Exponents are the features which well represent the EEG signals and the PNN trained on these features achieved high classification accuracies.
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recurrent neural networks employing Lyapunov Exponents for eeg signals classification
Expert Systems With Applications, 2005Co-Authors: Nihal Fatma Guler, Elif Derya Ibeyli, Inan GulerAbstract:There are a number of different quantitative models that can be used in a medical diagnostic decision support system including parametric methods, non-parametric methods and several neural network models. Unfortunately, there is no theory available to guide model selection. The aim of this study is to evaluate the diagnostic accuracy of the recurrent neural networks (RNNs) employing Lyapunov Exponents trained with Levenberg-Marquardt algorithm on the electroencephalogram (EEG) signals. An approach based on the consideration that the EEG signals are chaotic signals was used in developing a reliable classification method for electroencephalographic changes. This consideration was tested successfully using the non-linear dynamics tools, like the computation of Lyapunov Exponents. We explored the ability of designed and trained Elman RNNs, combined with the Lyapunov Exponents, to discriminate the EEG signals (EEG signals recorded from healthy volunteers with eyes open, epilepsy patients in the epileptogenic zone during a seizure-free interval, and epilepsy patients during epileptic seizures). The RNNs achieved accuracy rates which were higher than that of the feedforward neural network models. The obtained results demonstrated that the proposed RNNs employing the Lyapunov Exponents can be useful in analyzing long-term EEG signals for early detection of the electroencephalographic changes.
Dumitru Baleanu - One of the best experts on this subject based on the ideXlab platform.
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jacobian matrix algorithm for Lyapunov Exponents of the discrete fractional maps
Communications in Nonlinear Science and Numerical Simulation, 2015Co-Authors: Guocheng Wu, Dumitru BaleanuAbstract:Abstract The Jacobian matrix algorithm is often used to calculate the Lyapunov Exponents of the chaotic systems. This study extends the algorithm to discrete fractional cases. The tangent maps with memory effect are presented. The Lyapunov Exponents of one and two dimensional fractional logistic maps are calculated. The positive ones are used to distinguish the chaotic areas of the maps.
G A Leonov - One of the best experts on this subject based on the ideXlab platform.
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invariance of Lyapunov Exponents and Lyapunov dimension for regular and irregular linearizations
Nonlinear Dynamics, 2016Co-Authors: N V Kuznetsov, T A Alexeeva, G A LeonovAbstract:Nowadays the Lyapunov Exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic Exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov Exponents, LEs). In this work, the relation between Lyapunov Exponents and Lyapunov characteristic Exponents is discussed. The invariance of Lyapunov Exponents for regular and irregular linearizations under the change of coordinates is demonstrated.
