Determination of correlation spectra in chaotic systems

1990 ◽  
Vol 65 (17) ◽  
pp. 2087-2090 ◽  
Author(s):  
F. Christiansen ◽  
G. Paladin ◽  
H. H. Rugh
Keyword(s):  
Chaotic Systems

scholarly journals The State-space Model of Micro-chaos

2021 ◽  
Vol 15 ◽  
pp. 184-189
Author(s):  
Gabor Csernak ◽  
Gabor Stepan
Keyword(s):  
Chaotic Systems ◽  
Initial Conditions ◽  
State Space Model ◽  
Unstable State ◽  
Considerable Influence ◽  
Chaotic Oscillations ◽  
Controlled System ◽  
Space Model ◽  
Digitally Controlled

Micro-chaos is the phenomenon when the sampling, the delay and the round-off lead to small amplitude chaotic oscillations in a digitally controlled system. It has been proved mathematically during the last few years in a couple of simple cases that the evolving vibrations are indeed chaotic. In this study, we partially generalize these results to the case when an originally unstable state of a system is stabilized by digital feedback control. It is pointed out that this type of systems are sensitive to initial conditions and there exists a finite attracting domain in their phase-space. We also show that the oscillations, related to micro-chaos may have a considerable influence on the accuracy and settling time of the control system. The application of numerical techniques is unavoidable in the case of chaotic systems. Several possibilities are highlighted in the paper for the numerical determination of important characteristics of microchaotic oscillations.

scholarly journals Microwave experiments in the realm of fidelity

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150158 ◽  
Author(s):  
U. Kuhl
Keyword(s):  
Weak Coupling ◽  
Chaotic Systems ◽  
Review Article ◽  
Main Ingredient ◽  
Local Boundary ◽  
Global And Local ◽  
Fidelity Decay ◽  
Boundary Perturbations

In this review article, we will demonstrate the power of microwave experiments in the realm of fidelity also known as Loschmidt echoes. As the determination of the fidelity itself is experimentally tedious and error prone, we will introduce the scattering fidelity which under the conditions of chaotic systems and weak coupling approaches the fidelity itself. The main ingredient in fidelity investigations is the type and strength of a perturbation. The perturbations presented here will be both global and local boundary perturbations, as well as local perturber movements but also the change of coupling to the environment. All these perturbations will produce their own fidelity decay as a function of the perturbation strength, which will be discussed in this article.

INVESTIGATING CHAOTIC BEHAVIOR IN ECONOMIC SERIES: THE DELAY TIME IN THE GRASSBERGER–PROCACCIA ALGORITHM

1999 ◽  
Vol 02 (04) ◽  
pp. 357-380 ◽  
Author(s):  
TERESA APARICIO ◽  
EDUARDO POZO ◽  
DULCE SAURA
Keyword(s):  
Singular Value Decomposition ◽  
Delay Time ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Singular Value ◽  
Time Parameter ◽  
Practical Application ◽  
Second Stage ◽  
Value Decomposition

In this paper we try to bring forward evidence on the practical application of the Grassberger–Procaccia algorithm, in particular on the determination of the "delay time" parameter. For this purpose, we analyze the results obtained from applying the main methods proposed to calculate this delay time for series simulated from well-known chaotic systems. As the most relevant result we conclude that, in general, all the methods display inadequate behavior, except for that based on the previous filtering of the series according to singular value decomposition. In a second stage we apply the same study to three financial series, with the results appearing to confirm the advantage of this method.

Determination of Unstable Limit Cycles in Chaotic Systems by the Method of Unrestricted Harmonic Balance

1991 ◽  
Vol 46 (6) ◽  
pp. 499-502 ◽  
Author(s):  
Klaus Neymeyr ◽  
Friedrich Franz Seelig
Keyword(s):  
Chaotic System ◽  
Limit Cycles ◽  
Harmonic Balance ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Method Of Harmonic Balance ◽  
The Lorenz System

AbstractThe method of unrestricted harmonic balance (UHB) which is a generalization of the old method of harmonic balance and that was developed in preceding papers, is mathematically refined and applied to the evaluation of unstable limit cycles. The method is demonstrated for the case of the best investigated chaotic system, namely the Lorenz system. Some representative results are given

Galactic orbits of stars

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley
Keyword(s):  
Globular Cluster ◽  
Potential Field ◽  
High Velocity ◽  
Velocity Vector ◽  
Variable Stars ◽  
The Sun ◽  
Proper Motions ◽  
Rr Lyrae ◽  
The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

Distance to SN 1987A and the LMC

1999 ◽  
Vol 190 ◽  
pp. 549-554
Author(s):  
Nino Panagia
Keyword(s):  
Angular Size ◽  
Large Magellanic Cloud ◽  
Magellanic Cloud ◽  
Light Curves ◽  
Distance Modulus ◽  
Absolute Size ◽  
Sn 1987A

Using the new reductions of the IUE light curves by Sonneborn et al. (1997) and an extensive set of HST images of SN 1987A we have repeated and improved Panagia et al. (1991) analysis to obtain a better determination of the distance to the supernova. In this way we have derived an absolute size of the ringRabs= (6.23 ± 0.08) x 1017cm and an angular sizeR″ = 808 ± 17 mas, which give a distance to the supernovad(SN1987A) = 51.4 ± 1.2 kpc and a distance modulusm–M(SN1987A) = 18.55 ± 0.05. Allowing for a displacement of SN 1987A position relative to the LMC center, the distance to the barycenter of the Large Magellanic Cloud is also estimated to bed(LMC) = 52.0±1.3 kpc, which corresponds to a distance modulus ofm–M(LMC) = 18.58±0.05.

International determination of the total motion of the pole

1961 ◽  
Vol 13 ◽  
pp. 29-41
Author(s):  
Wm. Markowitz
Keyword(s):  
Secular Motion ◽  
The Future

A symposium on the future of the International Latitude Service (I. L. S.) is to be held in Helsinki in July 1960. My report for the symposium consists of two parts. Part I, denoded (Mk I) was published [1] earlier in 1960 under the title “Latitude and Longitude, and the Secular Motion of the Pole”. Part II is the present paper, denoded (Mk II).

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

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