scholarly journals SOME CHARACTERIZATIONS OF DICHOTOMY FOR IMPULSIVE DYNAMIC SYSTEMS

2021 ◽  
Vol 12 (5) ◽  
pp. 28-39
Author(s):  
GULNAZ ATTA ◽  
AWAIS YOUNUS
Keyword(s):  
Dynamic Systems ◽  
Spectral Decomposition ◽  
Closed Subset ◽  
Decomposition Theorem ◽  
Classical Case ◽  
Dynamic Equations ◽  
Real Numbers

We study the problem of dichotomy and boundedness for impulsive dynamic equations on arbitrary closed subset of real numbers. The spectral decomposition theorem gives all our main results. The obtained results are fundamentally new, even for the classical case.

scholarly journals Quasi-shadowing for partially hyperbolic diffeomorphisms

2014 ◽  
Vol 35 (2) ◽  
pp. 412-430 ◽  
Author(s):  
HUYI HU ◽  
YUNHUA ZHOU ◽  
YUJUN ZHU
Keyword(s):  
Spectral Decomposition ◽  
Hyperbolic Systems ◽  
Decomposition Theorem ◽  
Closing Lemma ◽  
Shadowing Property ◽  
Hyperbolic Diffeomorphisms ◽  
Uniformly Hyperbolic Systems ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphisms ◽  
Partially Hyperbolic Diffeomorphism

AbstractA partially hyperbolic diffeomorphism $f$ has the quasi-shadowing property if for any pseudo orbit $\{x_{k}\}_{k\in \mathbb{Z}}$, there is a sequence of points $\{y_{k}\}_{k\in \mathbb{Z}}$ tracing it in which $y_{k+1}$ is obtained from $f(y_{k})$ by a motion ${\it\tau}$ along the center direction. We show that any partially hyperbolic diffeomorphism has the quasi-shadowing property, and if $f$ has a $C^{1}$ center foliation then we can require ${\it\tau}$ to move the points along the center foliation. As applications, we show that any partially hyperbolic diffeomorphism is topologically quasi-stable under $C^{0}$-perturbation. When $f$ has a uniformly compact $C^{1}$ center foliation, we also give partially hyperbolic diffeomorphism versions of some theorems which hold for uniformly hyperbolic systems, such as the Anosov closing lemma, the cloud lemma and the spectral decomposition theorem.

Artificial neural networks and adaptive neuro-fuzzy inference systems for parameter identification of dynamic systems

2020 ◽  
Vol 39 (5) ◽  
pp. 6145-6155
Author(s):  
Ramin Vatankhah ◽  
Mohammad Ghanatian
Keyword(s):  
Differential Equations ◽  
Dynamic Systems ◽  
Fuzzy Inference ◽  
Dynamic Equations ◽  
Control Analysis ◽  
Unknown Parameters ◽  
Inference System ◽  
Neuro Fuzzy ◽  
Artificial Neural ◽  
Inference Systems

There would always be some unknown geometric, inertial or any other kinds of parameters in governing differential equations of dynamic systems. These parameters are needed to be numerically specified in order to make these dynamic equations usable for dynamic and control analysis. In this study, two powerful techniques in the field of Artificial Intelligence (AI), namely Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) are utilized to explain how unknown parameters in differential equations of dynamic systems can be identified. The data required for training and testing the ANN and the ANFIS are obtained by solving the direct problem i.e. solving the dynamic equations with different known parameters and input stimulations. The governing ordinary differential equations of the system is numerically solved and the output values in different time steps are obtained. The output values of the system and their derivatives, the time and the inputs are given to the ANN and the ANFIS as their inputs and the unknown parameters in the dynamic equations are estimated as the outputs. Finally, the performances of the ANN and the ANFIS for identifying parameters of the system are compared based on the test data Percent Root Mean Square Error (% RMSE) values.

Treating Uncertainties in Multibody Dynamic Systems Using a Polynomial Chaos Spectral Decomposition

2004 ◽  
Author(s):  
Corina Sandu ◽  
Adrian Sandu ◽  
Brendan J. Chan ◽  
Mehdi Ahmadian
Keyword(s):  
Frequency Domain ◽  
Dynamic Systems ◽  
Time Domain ◽  
Spectral Decomposition ◽  
Polynomial Chaos ◽  
Model Uncertainties ◽  
Dynamic Simulations ◽  
Computational Tools ◽  
Model Complex ◽  
Multibody Dynamic

This study addresses the critical need for computational tools to model complex nonlinear multibody dynamic systems in the presence of parametric and external uncertainty. Polynomial chaos has been used extensively to model uncertainties in structural mechanics and in fluids, but to our knowledge they have yet to be applied to multibody dynamic simulations. We show that the method can be applied to quantify uncertainties in time domain and frequency domain.

scholarly journals A numerical view of spectral decomposition theorem for SFT

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
Dariusz Jabłoński
Keyword(s):  
Spectral Decomposition ◽  
Decomposition Theorem

AbstractIn this paper algorithmizable conditions of Spectral Decomposition Theorem for SFT are presented.

scholarly journals Solvability and Stability of Impulsive Set Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Shihuang Hong ◽  
Jing Gao ◽  
Yingzi Peng
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Difference Equations ◽  
Time Scale ◽  
Dynamic Equations ◽  
Stability Of Solutions ◽  
Real Numbers ◽  
Generalized Derivative ◽  
Special Cases ◽  
Existence And Stability

A class of new nonlinear impulsive set dynamic equations is considered based on a new generalized derivative of set-valued functions developed on time scales in this paper. Some novel criteria are established for the existence and stability of solutions of such model. The approaches generalize and incorporate as special cases many known results for set (or fuzzy) differential equations and difference equations when the time scale is the set of the real numbers or the integers, respectively. Finally, some examples show the applicability of our results.

scholarly journals ON I-ACCELERATION CONVERGENCE OF SEQUENCES OF FUZZY REAL NUMBERS

2012 ◽  
Vol 17 (4) ◽  
pp. 549-577 ◽  
Author(s):  
Amar Jyoti Dutta ◽  
Binod Chandra Tripathy
Keyword(s):  
Decomposition Theorem ◽  
Real Numbers ◽  
Different Types ◽  
Fuzzy Real Numbers ◽  
Convergence Of Sequences

In this article we introduce the notion of ideal acceleration convergence of sequences of fuzzy real numbers. We have proved a decomposition theorem for ideal acceleration convergence of sequences as well as for subsequence transformations and studied different types of acceleration convergence of fuzzy real valued sequence.

PREDICTIVE DECOMPOSITION OF SEISMIC TRACES

Geophysics ◽  
1957 ◽  
Vol 22 (4) ◽  
pp. 767-778 ◽  
Author(s):  
Enders A. Robinson
Keyword(s):  
Time Series ◽  
Regression Analysis ◽  
Spectral Decomposition ◽  
Past History ◽  
Decomposition Theorem ◽  
Time Sequence ◽  
The Other ◽  
Volume Control ◽  
Minimum Phase ◽  
Arrival Times

The generalized harmonic analysis, or spectral decomposition, of a time series results in its representation in terms of its harmonic, or sinusoidal, components. This paper, on the other hand, develops in an expository manner the generalized regression analysis, or predictive decomposition, of a time series. This decomposition results in the representation of the time series at any moment in terms of its own observable past history plus an unpredictable, random‐like innovation. For the purposes of this paper, it is assumed that a seismic trace (recorded with automatic volume control) is additively composed of many overlapping seismic wavelets which arrive as time progresses. It is assumed that each wavelet has the same stable, one‐sided, minimum‐phase shape and that the arrival times and strengths of these wavelets may be represented by a time sequence of uncorrelated random variables. By applying the predictive decomposition theorem, it is shown how the wavelet shape may be extracted from the trace, leaving as a residual the strengths of the wavelets at their respective arrival times.

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