• 충청수학회지
• /
• 제22권3호
• /
• pp.593-596
• /
• 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
• /
• 제24권3호
• /
• pp.375-395
• /
• 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
• /
• 제24권3호
• /
• pp.447-467
• /
• 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.

• 대한수학회논문집
• /
• 제22권4호
• /
• pp.575-586
• /
• 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.

• 대한전기학회논문지:전력기술부문A
• /
• 제48권12호
• /
• pp.1486-1491
• /
• 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.

• 한국정보처리학회논문지
• /
• 제6권7호
• /
• pp.1825-1831
• /
• 1999

카오스 이론의 프랙탈 차원과 어트랙터를 이용하여 특징을 추출하여 문자인식에 적용하는 새로운 방법을 제안함으로써 기존의 혼동문자에 의한 오인식 비율을 줄이고자 하였다. 먼저 인식기에 부담을 줄이기 위해서 각 문자에 대해 특징을 조사하여 분류를 행한다. 분류된 문자에 대해 각 문자에 해당하는 Box-counting dimension, Natural Measure, Information dimension을 구하여 특징을 추출하여 인식하였다. 또한 문자의 히스토그램의 값을 이용하여 어트랙터를 구성하고 어트랙터에서 차원 값을 구한 다음 문자 자체의 차원 값과 함께 특징으로 사용하여 인식하였다. 실험 결과 전체적인 인식율의 평균은 학습 데이터에 대해서는 평균 96.03%, 미학습 데이터에 대해서는 91.74%를 나타내어 제안된 방법의 유효성을 보였다.

• ETRI Journal
• /
• 제35권1호
• /
• pp.100-108
• /
• 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.

• 대한수학회지
• /
• 제54권3호
• /
• pp.773-791
• /
• 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.

• 대한수학회지
• /
• 제54권1호
• /
• pp.1-16
• /
• 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.

• 대한수학회보
• /
• 제51권5호
• /
• pp.1299-1324
• /
• 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.