scholarly journals Time-domain boundedness of noise-to-state exponentially stable systems

2020 ◽  
Vol 26 ◽  
pp. 105
Author(s):  
Zhou Fang ◽  
Chuanhou Gao
Keyword(s):  
Lower Bound ◽  
Exponential Stability ◽  
Time Domain ◽  
Domain Of Attraction ◽  
Stable System ◽  
Stochastic Noise ◽  
Exponentially Stable ◽  
Probability Domain ◽  
The Time Domain ◽  
Insight Into

In this paper we prove the time-domain boundedness for noise-to-state exponentially stable systems, and further make an estimation of its lower bound function, which allows to answer the question that how long the solution of a stochastic noise-to-state exponentially stable system stays in the domain of attraction and what happens with it if it escapes from this region for a while. The results will complement the probability-domain boundedness of noise-to-state exponentially stable systems, and provide a new insight into noise-to-state exponential stability.

scholarly journals Direct measurement of Coulomb-laser coupling

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Doron Azoury ◽  
Michael Krüger ◽  
Barry D. Bruner ◽  
Olga Smirnova ◽  
Nirit Dudovich
Keyword(s):  
Coulomb Interaction ◽  
Time Domain ◽  
Coulomb Potential ◽  
Laser Field ◽  
Large Range ◽  
Extreme Ultraviolet ◽  
Strong Field ◽  
The Time Domain ◽  
First Time ◽  
Insight Into

AbstractThe Coulomb interaction between a photoelectron and its parent ion plays an important role in a large range of light-matter interactions. In this paper we obtain a direct insight into the Coulomb interaction and resolve, for the first time, the phase accumulated by the laser-driven electron as it interacts with the Coulomb potential. Applying extreme-ultraviolet interferometry enables us to resolve this phase with attosecond precision over a large energy range. Our findings identify a strong laser-Coulomb coupling, going beyond the standard recollision picture within the strong-field framework. Transformation of the results to the time domain reveals Coulomb-induced delays of the electrons along their trajectories, which vary by tens of attoseconds with the laser field intensity.

scholarly journals Application of nonlinear dynamics methods for quantitative and qualitative evaluation of properties of 2D models of S-chaos

2021 ◽  
Vol 16 (91) ◽  
pp. 125-143
Author(s):  
Aleksei A. Gavrishev ◽  
Keyword(s):  
Nonlinear Dynamics ◽  
Lower Bound ◽  
Time Domain ◽  
Initial Conditions ◽  
Qualitative Evaluation ◽  
Recurrence Analysis ◽  
Combined Application ◽  
Student Version ◽  
The Time Domain ◽  
Property Characteristic

In this article, based on the mathematical, numerical and computer modeling carried out by the combined application of E&F Chaos, Past, Fractan, Visual Recurrence Analysis, Eviews Student Version Lite programs, some of the well-known 2D models of S-chaos are modeled, the data obtained are studied using nonlinear dynamics methods and the fact of their relation or non-relation to chaotic (quasi-chaotic) processes is established. As a result, it was found that the time diagrams obtained for the studied 2D models of S-chaos have a complex noise-like appearance and are continuous in the time domain. The resulting spectral diagrams have both a complex noise-like and regular appearance and are continuous in the spectral regions. The obtained values of BDS-statistics show that some of the time implementations can be attributed to chaotic (quasi-chaotic) processes. Also, the obtained values of BDS-statistics show that the studied 2D models of S-chaos have a property characteristic of classical chaotic (quasi-chaotic) processes: the slightest change in the initial conditions leads to the generation of a new set of signals. The obtained values of the lower bound of the KS-entropy show that the studied models also have the properties of chaotic (quasi-chaotic). Taking into account the conducted research and data from known works [1–5], it is possible to conclude that 2D models of S-chaos can relate to chaotic (quasi-chaotic) processes.

scholarly journals Preserving Global Exponential Stability of Hybrid BAM Neural Networks with Reaction Diffusion Terms in the Presence of Stochastic Noise and Connection Weight Matrices Uncertainty

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yan Li ◽  
Yi Shen
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Reaction Diffusion ◽  
Stochastic Noise ◽  
Bam Neural Networks ◽  
Connection Weight ◽  
Exponentially Stable ◽  
The Neural Networks ◽  
The Impact

We study the impact of stochastic noise and connection weight matrices uncertainty on global exponential stability of hybrid BAM neural networks with reaction diffusion terms. Given globally exponentially stable hybrid BAM neural networks with reaction diffusion terms, the question to be addressed here is how much stochastic noise and connection weights matrices uncertainty the neural networks can tolerate while maintaining global exponential stability. The upper threshold of stochastic noise and connection weights matrices uncertainty is defined by using the transcendental equations. We find that the perturbed hybrid BAM neural networks with reaction diffusion terms preserve global exponential stability if the intensity of both stochastic noise and connection weights matrices uncertainty is smaller than the defined upper threshold. A numerical example is also provided to illustrate the theoretical conclusion.

A Note on the Lyapunov Stability of Fractional-Order Nonlinear Systems

2017 ◽  
Author(s):  
Sara Dadras ◽  
Soodeh Dadras ◽  
Hadi Malek ◽  
YangQuan Chen
Keyword(s):  
Exponential Stability ◽  
Fractional Order ◽  
Lyapunov Stability ◽  
Time Domain ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Sufficient Condition ◽  
Fractional Order Systems ◽  
The Stability ◽  
The Time Domain

In this paper, stability of fractional order (FO) systems is investigated in the sense of the Lyapunov stability theory. A new definition for exponential stability of the fractional order systems is given and sufficient conditions are obtained for the exponential stability of the FO systems using the notion of Lyapunov stability. Besides, a less conservative sufficient condition is derived for asymptotical stability of FO systems. The stability analysis is done in the time domain. Numerical examples are given to show that the obtained conditions are effective and applicable in practice.

On: “Induced‐polarization effects in time‐domain electromagnetic measurements” by M. F. Flis, G. A. Newman, and G. W. Hohmann (GEOPHYSICS, 54, 514–523, April 1989).

Geophysics ◽  
1989 ◽  
Vol 54 (12) ◽  
pp. 1655-1656 ◽  
Author(s):  
Richard Smith
Keyword(s):  
Time Domain ◽  
Three Dimensional ◽  
Polarization Current ◽  
Electromagnetic Measurements ◽  
Charging Current ◽  
Time Domain Electromagnetic ◽  
Time Domain Response ◽  
The Time Domain ◽  
Theoretical Results ◽  
Insight Into

Flis et al. provide useful insight into the time‐domain response of three‐dimensional polarizable bodies; however, their inference that negative transients are caused by a polarization current which reverses direction disagrees with the previously published theoretical results of Smith et al. (1988) and Smith and West (1988), who found that the polarization current is always negative (provided that the chargeability m and charging current are positive).

Apodisation in the time domain

1992 ◽  
Vol 2 (4) ◽  
pp. 615-620
Author(s):  
G. W. Series
Keyword(s):  
Time Domain ◽  
The Time Domain

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

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