• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.579-600
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• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.357-378
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• 2012

In this paper, we consider the convective Cahn-Hilliard equation. Based on the regularity estimates for the semigroups, iteration technique and the classical existence theorem of global attractors, we prove that the convective Cahn-Hilliard equation possesses a global attractor in $H^k$($k\geq0$) space, which attracts any bounded subset of $H^k({\Omega})$ in the $H^k$-norm.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.631-638
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• 2005

we prove that, given any compact metric space X, there exists a residual subset R of H(X), the space of all homeomorphisms on X, such that if $\in$ R has a totally chain-transitive attractor A, then any g sufficiently close to f has a totally chain transitive attractor A$\_{g}$ which is convergent to A in the Hausdorff topology.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.631-639
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• 2013

We investigate the existence of a global attractor for the Cauchy problem $$x^{\prime}(t)=Ax(t)+F(x(t)),\;x(0)=x_0{\in}X$$ on a Banach space X according to the remark in You and Yuan's paper.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1469-1484
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• 2014

In this paper we are concerned with a class of stochastic partial functional differential equations with infinite delay. Supposing that the linear part is a Hille-Yosida operator but not necessarily densely defined and employing the integrated semigroup and random dynamics theory, we present some appropriate conditions to guarantee the existence of a random attractor.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.143-159
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• 2013

This paper is concerned with the long time behavior for the solution semiflow of the coupled two-compartment Gray-Scott equations with the homogeneous Neumann boundary condition on a bounded domain of space dimension $n{\leq}3$. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the equations possesses a global attractor in $H^k({\Omega})^4$ ($k{\geq}0$) space.

• 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.

• 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.

• 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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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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.