• Nuclear Engineering and Technology
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• v.48 no.2
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• pp.434-447
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• 2016

The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.1
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• pp.171-179
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• 2001

The purpose of this paper is the derivation and development of the new definitions and methods for the new estimation of robustness for the systems having structured uncertainties. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. The systems considered are assumed to be nominally linear, with time-variant, nonlinear bounded perturbations. This new techniques demonstrate the improvement of robustness bounds from the numerical results.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.43.1-43
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• 2001

We propose two control methods of the Lyapunov exponents for Jordan-type recurrent neural networks. Both the two methods are formulated by a gradient-based learning method. The first method is derived strictly from the definition of the Lyapunov exponents that are represented by the state transition of the recurrent networks. The first method can control the complete set of the exponents, called the Lyapunov spectrum, however, it is computationally expensive because of its inherent recursive way to calculate the changes of the network parameters. Also this recursive calculation causes an unstable control when, at least, one of the exponents is positive, such as the largest Lyapunov exponent in the recurrent networks with chaotic dynamics. To improve stability in the chaotic situation, we propose a non recursive formulation by approximating ...

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.129-135
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• 2000

We show that a compact subset M of X is asymptotically stable if and only if a strict Lyapunov function of M exists.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.09a
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• pp.108-108
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• 1995

• Proceedings of the KIEE Conference
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• 1985.07a
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• pp.89-91
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• 1985

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.700-705
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• 2005

The purpose of this project is the derivation and development of techniques for the new estimation of robustness for the systems having uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. Bounded means the uncertainties are with same positive/negative range. The number of uncertainties will be the degree of freedoms in the calculation of the stability region. This is so called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, the selection of Lyapunov candidate function is of various forms. In this paper, the quadratic form is selected. this generated techniques has been demonstrated by recent research interest in the area of robust control design and confirms that estimation of robustness bounds will be improved upon those obtained by results of the original Lyapunov method. In this paper, the symbolic algebraic procedures are utilized and the calculating errors are reduced in the numerical procedures. The application of numerical procedures can prove the improvements in estimations of robustness for one-and more structured perturbations. The applicable systems is assumed to be linear with time-varying with nonlinear bounded perturbations. This new techniques will be extended to other nonlinear systems with various forms of uncertainties, especially in the nonlinear case of the unstructured perturbations and also with various control method.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.371-381
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• 2017

There has never been research on Chaos analysis using real estate auction sale price rate in Korea. In this study, three Chaos analysis methodologies - Hurst exponent, correlation dimension, and maximum Lyapunov exponent - in order to capture the nonlinear deterministic dynamic system characteristics. High level of Hurst exponent and the extremely low maximum Lyapunov exponent provide the tendency and the persistence of the data. The empirical results give two meaningful facts. First, monthly time lags of the correlation dimension are coincident with the time period from the approval auction start day to the sale price fixing day. Second, its weekly time lags correspond to the time period from the last day of request for sale price allocation to the sale price fixing day. Then, this study potentially examines the predictability of the real estate auction price rate time series.

• Annals of Clinical Neurophysiology
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• v.8 no.2
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• pp.135-145
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• 2006

Background: Parkinson's disease is movement disorder due to dopaminergic deficiency. It has been noted that cognitive dysfunction also presented on Parkinson's disease patients. But, it is not clear whether such a cognitive dysfunction was a dopaminergic dysfunction or cholinergic dysfunction. Using linear and non-linear analyses, we analysed the effect of cognitive and motor symptom on EEG change. Methods: EEGs were recorded from patients with Parkinson's disease and essential tremor, and normal controls during rest. We calculated the power spectrum, correlation dimension and Lyapunov exponent by using 'Complexity'program. The power spectrum, correlation dimension, and Lyapunov exponent were compared between Parkinson's disease patients and essential tremor patients. Results: Theta power was increased in Parkinson's disease patient group. Correlation dimension was increased in Parkinson's disease patients. Positive correlation was noted between MMSE and correlation dimension, and negative correlation was noted between MMSE and Lyapunov exponent. Lyapunov exponent was decreased in Parkinson's disease patient. Conclusions: We conclude that the state of Parkinson's disease patient is characterized by increased correlation dimension and decreased Lyapunov exponent.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.657-664
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• 2000

A new concept of stability that includes Lyapunov and orbital stabilities and leads to concepts in between them is discussed in terms of a given topology of the function space. The criteria for such new concepts to hold are investigted employing suitably Lyapunov-like functions and the comparison principle.