• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.423-443
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• 2022

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on ℝ^N. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic a priori estimate method.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1279-1298
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• 2021

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

• Speech Sciences
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• v.10 no.2
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• pp.45-55
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• 2003

Strange attractor can be used as a presentation method for signal processing. Fractal dimension is well known method that extract features from attractor. Even though the method provides powerful capabilities for speech processing, there is drawback which should be solved in advance. Normally, the size of the raw signal should be long enough for processing if we use the fractal dimension method. However, in the area of connected-digits problem, normally, syllable or semi-syllable based processing is applied. In this case, there is no evidence that we have sufficient data or not to extract characteristics of attractor. This paper discusses the relationship between the size of the signal data and the calculation result of fractal dimension, and also discusses the efficient way to be applied to connected-digit recognition.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.1
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• pp.158-164
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• 2002

This paper proposes the optimization of ultrasonic signal recognition in ferrite carbon steel weld zone using neural networks. For these purposes, the ultrasonic signals for defects as porosity, incomplete penetration and slag inclusion in the weld zone are acquired in the type of time series data. And then their applications evaluated feature extraction based on the time-frequency-attractor domain(peak to peak, rise time, rise slope, fall time, fall slope, pulse duration, power spectrum, and bandwidth) and attractor characteristics (fractal dimension and attractor quadrant) etc. The proposed neural networks system in this study can enhances performance of ultrasonic signal recognition.

• Speech Sciences
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• v.9 no.2
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• pp.147-155
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• 2002

In the area of speech processing, raw signals used to be presented into 2D format. However, such kind of presentation methods have limitation to extract characteristics from the signal because of the presentation method. Generally, not much information can be detected from the 2D signal. Strange attractor in the field of chaos theory provides a 3D presentation method. In the area of recognition problem, signal presentation method is very important because good features can be detected from a good presentation. This paper discusses a new feature extraction method that extracts features from a cycle of the strange attractor. A neural network is used to check whether the method extracts suitable features or not. The result shows very good points that can be applied to some areas of signal processing.

• The Journal of the Acoustical Society of Korea
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• v.13 no.2E
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• pp.26-31
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• 1994

A new feature extraction technique utilizing strange attractor and artificial neural network for speaker recognition is presented. Since many signals change their characteristics over long periods of time, simple time-domain processing techniques should e capable of providing useful information of signal features. In many cases, normal time series can be viewed as a dynamical system with a low-dimensional attractor that can be reconstructed from the time series using time delay. The reconstruction of strange attractor is described. In the technique, the raw signal will be reproduced into a geometric three dimensional attractor. Classification decision for speaker recognition is based upon the processing or sets of feature vectors that are derived from the attractor. Three different methods for feature extraction will be discussed. The methods include box-counting dimension, natural measure with regular hexahedron and plank-type box. An artificial neural network is designed for training the feature data generated by the method. The recognition rates are about 82%-96% depending on the extraction method.

• Korean Journal of Mathematics
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• v.9 no.1
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• pp.67-73
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• 2001

For some equation related with exponential function, we seek roots and find the properties of the roots. By using the relation of the roots and attractors, we find a region in the basin of attraction of the attractor at infinity for Newton's method for solving given equation.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.273-283
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• 2000

In this paper we consider two delay equations with in-finite delay. We will give two sufficient conditions for the positive and zero equilibriums of these equations to be a global attractor respectively.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2001.05a
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• pp.711-714
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• 2001

We present a detailed analysis of the behavior of a multiple-attractor cellular automata.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.53-62
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• 2002

In this paper we analyze the behavior of linear multiple attractor cellular automata having two-predecessors.