Boundary of Stability Region: Theoretical Results

2013 ◽  
pp. 327-329
Keyword(s):  
Stability Region ◽  
Boundary Of Stability ◽  
Theoretical Results

NEW RESULTS ABOUT ROUTE TO CHAOS IN ROSSLER SYSTEM

2004 ◽  
Vol 14 (01) ◽  
pp. 293-308 ◽  
Author(s):  
SVETOSLAV NIKOLOV ◽  
VALKO PETROV
Keyword(s):  
Bifurcation Analysis ◽  
Stability Region ◽  
Analytical Formula ◽  
Stability Loss ◽  
Transition To Chaos ◽  
Rossler System ◽  
Rössler System ◽  
Route To Chaos ◽  
Boundary Of Stability

In this paper, the theory of Lyapunov–Andronov is applied to investigate the route to chaos in Rossler system. On the base of a new analytical formula for the first Lyapunov value at the boundary of stability region, we make a detailed bifurcation analysis of this system. From the obtained results the following new conclusions are made: Transition to chaos in the Rossler's system takes place at soft stability loss in the form of a cascade of periodic self-oscillations. Then the occurrence of chaotic self-oscillations in this system takes place under hard stability loss.

Boundary of stability region of a thin-walled beam under complex loading condition

2017 ◽  
Vol 122 ◽  
pp. 355-361 ◽  
Author(s):  
Phung Van Binh ◽  
Dang Hoang Minh ◽  
Gavriushin Sergei Sergeevich ◽  
Nguyen Viet Duc
Keyword(s):  
Stability Region ◽  
Loading Condition ◽  
Complex Loading ◽  
Thin Walled ◽  
Boundary Of Stability

Configuration and Robustness in Visual Servo

2004 ◽  
Vol 16 (2) ◽  
pp. 178-185 ◽  
Author(s):  
Graziano Chesi ◽  
◽  
Koichi Hashimoto
Keyword(s):  
Local Stability ◽  
Stability Region ◽  
Visual Servoing ◽  
Eye Position ◽  
Visual Servo ◽  
Control Laws ◽  
Extrinsic Parameters ◽  
Point To Point ◽  
The Stability ◽  
Theoretical Results

Effects of camera calibration errors on the point-to-point task are investigated in static-eye and hand-eye visual servoing realized with position-based and image-based control laws. For these four configurations, the effect of uncertainty on the extrinsic parameters is analyzed. The results show local stability for all configurations under small calibration errors. However, a steady state error is found in the hand-eye position-based configuration. Simulations have been done to confirm the theoretical results and evaluate the effects of the uncertainty in terms of stability region. Another contribution of the paper consists of providing a method for estimating the stability region robust against uncertainty directions for the static-eye position-based case with uncertainty on the camera centers.

scholarly journals Delay Cournot Duopoly Game with Gradient Adjustment: Berezowski Transition from a Discrete Model to a Continuous Model

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 32
Author(s):  
Akio Matsumoto ◽  
Ferenc Szidarovszky ◽  
Keiko Nakayama
Keyword(s):  
Stability Region ◽  
Period Doubling ◽  
Continuous Model ◽  
Delay Model ◽  
Chaotic Oscillations ◽  
Cournot Duopoly ◽  
Numerical Studies ◽  
Inertia Coefficient ◽  
The Stability ◽  
Theoretical Results

This paper investigates the asymptotical behavior of the equilibrium of linear classical duopolies by reconsidering the two-delay model with two different positive delays. In a two-dimensional analysis, the stability switching curves were first analytically determined. Numerical studies verified and illustrated the theoretical results. In the sensitivity analysis it was demonstrated that the inertia coefficient has a twofold effect: enlarges the stability region as well as simplifies the complicated dynamics with period-halving cascade. In contrary, the adjustment speed contracts the stability region and complicates simple dynamics with period-doubling bifurcation. In addition, for various values of τ1 and τ2, a wide variety of dynamics appears ranging from simple cycle via a Hopf bifurcation to chaotic oscillations.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Investigating the Nonlinear Optical Response of Pepper Oil under Low Power Irradiation with Continuous Wave Visible Laser Beam

2020 ◽  
pp. 131-138
Keyword(s):  
Refractive Index ◽  
Nonlinear Refractive Index ◽  
Nonlinear Optical ◽  
Continuous Wave ◽  
Diffraction Integral ◽  
Visible Laser ◽  
Limiting Property ◽  
Kirchhoff Diffraction Integral ◽  
Theoretical Results ◽  
Good Agreement

The nonlinear optical properties of pepper oil are studied by diffraction ring patterns and Z-scan techniques with continuous wave beam from solid state laser at 473 nm wavelength. The nonlinear refractive index of the sample is calculated by both techniques. The sample show high nonlinear refractive index. Based on Fresnel-Kirchhoff diffraction integral, the far-field intensity distributions of ring patterns have been calculated. It is found that the experimental results are in good agreement with the theoretical results. Also the optical limiting property of pepper oil is reported. The results obtained in this study prove that the pepper oil has applications in nonlinear optical devices.

70 years of ITEP: some theoretical results

2016 ◽  
Vol 186 (8) ◽  
pp. 869-878
Author(s):  
Mikhail I. Vysotskii ◽  
Aleksandr D. Dolgov ◽  
Viktor A. Novikov
Keyword(s):  
Theoretical Results

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

2020 ◽  
Vol 7 (3) ◽  
pp. 52-56
Author(s):  
MMATMATISA JALILOV ◽  
◽  
RUSTAM RAKHIMOV ◽  
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Three Dimensional ◽  
Viscoelastic Plate ◽  
Constant Thickness ◽  
Regional Problem ◽  
Rigid Contact ◽  
Under Construction ◽  
Derivatives Of ◽  
Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

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