• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.593-596
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• 2009

In this short note, we explicate a relation among Collet-Eckmann attractors, Lyapunov attractors and asymptotically stable attractors in the sense of J. Milnor[4].

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.375-395
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• 2016

In this paper, we study the long-time dynamical behavior for the extensible suspension bridge equations with past history. We prove the existence of the global attractors by using the contraction function method. Furthermore, the regularity of global attractor is achieved.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.447-467
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• 2016

We prove the existence of random attractors for the continuous random dynamical systems generated by stochastic damped plate equations with linear memory and additive white noise when the nonlinearity has a critically growing exponent.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.575-586
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• 2007

We introduce here notions of chain recurrent sets, attractors and its basins for general dynamical systems and prove important properties including (i) the chain recurrent set CR(f) of f on a metric space (X, d) is the complement of the union of sets B(A) -A as A varies over the collection of attractors and (ii) genericity of general dynamical systems.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.12
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• pp.1486-1491
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• 1999

This paper presents a method of recognizing high impedance fault(HIF) of electrical power systems and classifying fault patterns based on chaos attractors. Two dimensional chaos attractors are reconstructed from neutral point current waveforms. Reliable features for HIF pattern classification are obtained from the chaos attractors. Radial basis function network, trained with two types of HIF data generated by the electromagnetic transient program and measured form actual faults. The RBFN successfully classifies normal and the three types of fault patterns according to the features generated from the chaos attractors.

• The Transactions of the Korea Information Processing Society
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• v.6 no.7
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• pp.1825-1831
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• 1999

In this paper, to reduce misrecognized characters, we propose the new method that extract features from character to apply to the character recognition using features from character to apply to the character recognition using fractal dimensions and attractors. Firstly, to reduce the load of recognizer we classify the characters. For the classified character, we extract the features for Box-counting dimensions. Natural Measures, Information dimensions then recognize characters. With histogram, we generate attractors and calculate dimensions from attractors. Then we recognize characters with dimensions of characters and attractors. An experimental result that the overall recognition rates for the training data and testing data are 96.03% and 91.74% respectively. This result shows the effectiveness of proposed method.

• ETRI Journal
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• v.35 no.1
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• pp.100-108
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• 2013

In this paper, a feature extraction (FE) method is proposed that is comparable to the traditional FE methods used in automatic speech recognition systems. Unlike the conventional spectral-based FE methods, the proposed method evaluates the similarities between an embedded speech signal and a set of predefined speech attractor models in the reconstructed phase space (RPS) domain. In the first step, a set of Gaussian mixture models is trained to represent the speech attractors in the RPS. Next, for a new input speech frame, a posterior-probability-based feature vector is evaluated, which represents the similarity between the embedded frame and the learned speech attractors. We conduct experiments for a speech recognition task utilizing a toolkit based on hidden Markov models, over FARSDAT, a well-known Persian speech corpus. Through the proposed FE method, we gain 3.11% absolute phoneme error rate improvement in comparison to the baseline system, which exploits the mel-frequency cepstral coefficient FE method.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.773-791
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• 2017

In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.1-16
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• 2017

In this paper we study a four dimensional tourism-based social-ecological dynamical system. In fact we analyse tourism profitability, compatibility and sustainability by using bifurcation theory in terms of structural properties of attractors of system. For this purpose first we transformed it into a three dimensional system such that the reduced system is the extended and modified model of the previous three dimensional models suggested for tourism with the same dimension. Then we investigate transcritical, pitchfork and saddle-node bifurcation points of system. And numerically by finding some branches of stable equilibria for system show the profitability of tourism industry. Then by determining the Hopf bifurcation points of system we find a family of stable attractors for that by numerical techniques. Finally we conclude the existence of these stable limit cycles implies profitability and compatibility and then the sustainability of tourism.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1299-1324
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• 2014

We prove the existence of uniform attractors $\mathcal{A}_{\varepsilon}$ in the space $H^1(\mathbb{R}^N){\cap}L^p(\mathbb{R}^N)$ for the following non-autonomous nonclassical diffusion equations on $\mathbb{R}^N$, $$u_t-{\varepsilon}{\Delta}u_t-{\Delta}u+f(x,u)+{\lambda}u=g(x,t),\;{\varepsilon}{\in}(0,1]$$. The upper semicontinuity of the uniform attractors $\{\mathcal{A}_{\varepsilon}\}_{{\varepsilon}{\in}[0,1]}$ at ${\varepsilon}=0$ is also studied.