• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.595-604
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• 2012

In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefore, Lyapunov exponents can decide whether an orbit is chaos or not. To measure the sensitive dependence on initial conditions for nonsmooth dynamical systems, the calculation of Lyapunov exponent plays a key role, but in a theoretical point of view or based on the definition of Lyapunov exponents, Lyapunov exponents of nonsmooth orbit could not be calculated easily, because the Jacobian derivative at some point in the orbit may not exists. We use an algorithmic calculation method for computing Lyapunov exponents using time series for a two dimensional piecewise smooth dynamic system.

• The Journal of the Society of Korean Medicine Diagnostics
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• v.11 no.2
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• pp.116-127
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• 2007

Background and Purpose: Acording to chaos theory, irregular signals of electroencephalogram can interpretated by nonlinear method. Chaotic nonlinear dynamics in EEG can be studied by calculating the correlation dimension. The aim of this study is to analyze EEG by correlation dimension and do Correlation Analysis of correlation dimension and cold-heat score Method: EEG raw data were measured during 15 minutes and choosed 40 seconds. We calculated correlation dimension and used surrogate data method for checking nonlinear data. After then do correlation analysis Result and Conclusion: Correlation dimension of channel 7 and channel 8 are showed significant correlation with cold score.

• The Journal of the Society of Korean Medicine Diagnostics
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• v.11 no.2
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• pp.68-83
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• 2007

Background and Purpose: According to chaos theory, irregular signals of electroencephalogram can interpretated by nonlinear method. Chaotic nonlinear dynamics in EEG can be studied by calculating the correlation dimension. The aim of this study is to analyze EEG by correlation dimension and do Correlation Analysis of correlation dimension and K-POMS factors score. Method: EEG raw data were measured during 15 minutes and choosed 40 seconds. We calculated correlation dimension and used surrogate data method for checking nonlinear data. After then do correlation analysis. Result and Conclusion: Correlation dimension of channel 6, channel 7 and channel 8 are showed significant correlation with vigor factor.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.643-650
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• 2014

A chaotic vibration isolation system is designed according to the chaotic vibration theory in this paper. The strong nonlinearity is generated by the system. Line spectra in the radiated noise maybe easily detected caused by marine vessels. It is Important to reduce the line spectra by improving the acoustic stealth of marine vessels. A multi-degree-freedom (MDF) nonlinear vibration isolation system (NVIS) system is setup by the experiment and finite element method. The model is established with finite element method. The results show that the behavior of the device gradually varies from period bifurcation into chaotic state and the line spectrum is changed from single spectral structure into broadband spectral structure. It is concluded that chaotic vibration isolation is preferable contrasted on line spectra isolation.

• International Journal of Internet, Broadcasting and Communication
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• v.15 no.2
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• pp.175-180
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• 2023

Fractal geometry, a relatively new branch of mathematics, was first introduced by Benoit Mandelbrot in 1975. Since then, its applications have expanded into various fields of natural science. In fact, it has been recognized as one of the three significant scientific discoveries of the mid-20th century, along with the Dissipative System and Chaos Theory. With the help of fractal geometry, designers can create intricate and expressive artistic patterns, using the concept of self-similarity found in nature. The impact of fractal geometry on the digital art world is significant and its exploration could lead to new avenues for creativity and expression. This paper aims to explore and analyze the development and applications of fractal geometry in digital art design. It also aims to showcase the benefits of applying fractal geometry in art creation and paves the way for future research on sacred geometry.

• Korean Journal of Biological Psychiatry
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• v.4 no.1
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• pp.67-73
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• 1997

The changes of electroencephalogram(EEG) in patients with dementia are most commonly studied by analyzing power or magnitude in certain traditionally defined frequency bands. However because of the absence of an identified metric which quantifies the complex amount of information, there are many limitations in using such a linear method. According to chaos theory, irregular signals of EEG can also result from low dimensional deterministic chaos. Chaotic nonlinear dynamics in the EEG can be studied by calculating the correlation dimension. The authors have analyzed EEG epochs from three patients with dementia of Alzheimer type and three matched control subjects. The multichannel correlation dimension is calculated from EEG epochs consisting of 15 channels with 16,384 data points per channel. The results showed that patients with dementia of Alzheimer type had significantly lower correlation dimension than non-demented controls on 12 channels. Topographic analysis showed that the correlation dimensions were significantly lower in patients with Alzheimer's disease on frontal, temporal, central, and occipital head regions. These results show that brains of patients with dementia of Alzheimer type have a decreased complexity of electrophysiological behavior. We conclude that the nonlinear analysis such as calculating correlation dimension can be a promising tool for detecting relative changes in the complexity of brain dynamics.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.1 s.94
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• pp.141-149
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• 1999

어느 한 계가 양수의 발산지수(Lyapunov exponent)를 가질 때 이 계는 카오스계로 분류되며 그 동특성은 예측이 불가능해 진다. 감쇠 기계계(소산계)에서는 위상공간(phase space)의 초기 부피가 시간에 따라 수축한다. 발산 지수들의 합은 음수이며 그 기계계의 감쇠와 관련되며, 따라서 발산지수들의 합은 감쇠의 변화를 감시하는데 사용되어질 수 있다. 그러나 그 감쇠변화를 감시하기 위해서는 발산지수를 계산하는데 사용하는 신호(data) 부분(segment)이 짧아야 한다. 이는 문제점을 야기시키는데 그 이유는 발산지수가 아주 많은 양의 발산률(divergence rate)의 평균으로서 구해지기 때문이다. 이 문제를 극복하기 위해서, 본 저자는 '순간발산지수(Instantaneous Lyapunov Exponent)'를 도입하였으며, 이 순간발산지수들의 합이 어떻게 기계계의 감쇠와 관련되어지는 가에 대하여 기술하였다. 미분방적식과 시계열(time series)을 이용한 컴퓨터 시뮬레이션은 '순간발산지수들의 합'의 중요성을 입증하였다. 그러나 시계열(또는 실험신호)로 부터의 정확한 순간발산지수를 측정하기는 매우 힘들기 때문에 '부분발산지수(Short term averaged Lyapunov Exponent)'를 또한 도입하였다.

• Journal of Korea Multimedia Society
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• v.6 no.1
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• pp.89-96
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• 2003

This paper propose the new method witch is adopted in extracting character features and recognizing numeric characters using fractal dimension and modified Henon Attractor of the Chaos Theory. Firstly, it gets features of mesh feature, projection feature and cross distance feature from numeric character images And their feature hi converted into time series data. Then using the modified Henon system suggested in this paper, it gets last features of numeric character image after calculating Natural Measure and information bit which art meant fractal dimension. Finally, numeric character recognition is performed by statistically finding out the each information bit showing the minimum difference against the normalized pattern database. An Experimental result shows 100% character classification rates for 10 digits and 90% of recognition rates in real situation and the recognition speed was 26 characters per second.

• Proceedings of the Korea Contents Association Conference
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• 2007.11a
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• pp.667-671
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• 2007

Moebius' L,INCAL Analysis of 'self' and 'self-consciousness' in philosophic viewpoint. In this research, I studies and analyzed Mobius' L,INCAL who had affected revitalization of Europe and America's genre cartoon and graphic novel. Among the L,INCAL. I selected some parts which are related to 'self' and 'self-consciousness' of 융(Jung), 라캉(Lacan), chaos theory Because it is too extensive for me to do this. Cartoons filled with philosophy is likely to have a possibility to be seen by adults. The goal of this study is to make a coner stone which all the classes can enjoy various cultures with.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07b
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• pp.939-944
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• 2002

PD phenomena can be regarded as a deterministic dynamical process where PD should be occurred if the local electric field be reached to be sufficiently high. And thus, its mathematical model can be described by either difference equations or differential equations using several state variables obtained from the time sequential measured data of PD signals. These variables can provide rich and complex behavior of detectable time series, for which Chaos theory can be employed. In this respect, a new PD pattern recognition method is proposed and named as 'Chaotic Analysis of Partial Discharges (CAPD)' for this work. For this purpose, six types of specimen are designed and made as the models of the possible defects that may cause sudden failures of the underground power transmission cables under service, and partial discharge signals, generated from those samples, are detected and then analyzed by means of CAPD. Throughout the work, qualitative and quantitative properties related to the PD signals from different defects are analyzed by use of attractor in phase space, information dimensions ($D_0$ and D2), Lyapunov exponents and K-S entropy as well. Based on these results, it could be pointed out that the nature of defect seems to be identified more distinctively when the CAPD is combined with traditional statistical method such as PRPDA. Furthermore, the relationship between PD magnitude and the occurrence timing is investigated with a view to simulating PD phenomena.