• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.829-836
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• 2005

In this note, we introduce a new proof of the unique-ness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.505-518
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• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.327-335
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• 2004

In this paper, we reformulate a snapshot attractor([5]), ($K,\;\={\mu_{\iota}}$) generated by a random baker's map with a sequence of probability measures {\={\mu_{\iota}}} on K. We obtain bounds of the correlation dimensions of ($K,\;\={\mu_{\iota}}$) for all ${\iota}\;{\geq}\;1$.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1996.10a
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• pp.96-100
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• 1996

So far the analysis and modeling of cutting process is studied commonly assumed as being linear stochastic or chaotic without experimental verification. So we verified force signals of cutting process(ball end-milling) is low-dimensional chaos by calculating Lyapunov Exponents. reconstructing attractor using time delay coordinates and calcula-ting it's fractal dimension.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1331-1342
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• 2009

In this paper, we analyze the behavior of the state transition of nongroup CA with a single attractor over GF($2^p$)(p > 1), and propose the algorithm for the construction of the state transition diagram of a Single Attractor CA(SACA) over GF($2^p$) which is very different from the construction algorithm for the state transition diagram of GF(2) SACA.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.97-106
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• 2012

In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence o a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.621-632
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• 2014

In this paper, we study the dynamical behavior of the one-dimensional convective Cahn-Hilliard equation(CCHE) on a periodic cell [$-{\pi},{\pi}$]. We prove that as the control parameter passes through the critical number, the CCHE bifurcates from the trivial solution to an attractor. We describe the bifurcated attractor in detail which gives the final patterns of solutions near the trivial solution.

• Speech Sciences
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• v.1
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• pp.285-293
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• 1997

This paper was constructed to investigate strange attractor in considering speech which is regarded as chaos in that the random signal appears in the deterministic raising system. This paper searches for the delay time from AR model power spectrum for constructing fit attractor for speech signal. As a result of applying Taken's embedding theory to the delay time, an exact correlation dimension solution is obtained. As a result of this consideration of speech, it is found that it has more speaker recognition characteristic parameter, and gains a large speaker discrimination recognition rate.

• Journal of Biomedical Engineering Research
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• v.15 no.3
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• pp.347-354
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• 1994

This paper describes a diagnostic protocol of nonlinear dynamic characteristics of biological system using chaos theory. An integrated chaos analysis system for the diagnosis of biological system was designed. We suggest a procedure of attractor reconstruction for reliable qualitative and quantitative analysis. The effect of autonomic nervous system activity on heart rate variability with power spectral analysis and its characteristics of chaotic attractors are investigated. The results show the applicability to evaluate the mental and physical conditions using nonlinear characteristics of biological signal.

• Journal of Korea Multimedia Society
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• v.4 no.6
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• pp.518-523
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• 2001

This paper proposes the new method which is adopted in extracting character features and recognizing characters using fractal dimension of the Chaos theory which highly recolonizes a minute difference with strange attractor created from Henon system. This paper implements a high precision character recognition system. firstly, it gets features of mesh, projection and cross distance feature from character images. And their feature is converted into data of time series. Then using modified Henon system suggested in this paper, each characters attractor about standard Korean Character, KSC 5601 is reconstructed. Secondly, in order to analyze the Chaotic degree of each characters attractor, it gets last features of character image after calculating box-counting Dimension, Natural Measure, Information Bit, Information Dimension which are meant fractal dimension. An experimental result shows 97.49% character classification rates for 2350 Korean characters using proposed method in this paper.