• Title, Summary, Keyword: attractor

Search Result 195, Processing Time 0.053 seconds

GLOBAL ATTRACTOR FOR A SEMILINEAR PSEUDOPARABOLIC EQUATION WITH INFINITE DELAY

  • Thanh, Dang Thi Phuong
    • Communications of the Korean Mathematical Society
    • /
    • v.32 no.3
    • /
    • pp.579-600
    • /
    • 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.

THE EXISTENCE OF GLOBAL ATTRACTOR FOR CONVECTIVE CAHN-HILLIARD EQUATION

  • Zhao, Xiaopeng;Liu, Bo
    • Journal of the Korean Mathematical Society
    • /
    • v.49 no.2
    • /
    • pp.357-378
    • /
    • 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.

TOTALLY CHAIN-TRANSITIVE ATTRACTORS OF GENERIC HOMEOMORPHISMS ARE PERSISTENT

  • GHANE FATEMEH HELEN;FAKHARI ABBAS
    • Bulletin of the Korean Mathematical Society
    • /
    • v.42 no.3
    • /
    • pp.631-638
    • /
    • 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.

RANDOM ATTRACTOR FOR STOCHASTIC PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

  • You, Honglian;Yuan, Rong
    • Bulletin of the Korean Mathematical Society
    • /
    • v.51 no.5
    • /
    • pp.1469-1484
    • /
    • 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.

GLOBAL ATTRACTOR FOR COUPLED TWO-COMPARTMENT GRAY-SCOTT EQUATIONS

  • Zhao, Xiaopeng;Liu, Bo
    • Bulletin of the Korean Mathematical Society
    • /
    • v.50 no.1
    • /
    • pp.143-159
    • /
    • 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.

Fractal Dimension Method for Connected-digit Recognition (연속음 처리를 위한 프랙탈 차원 방법 고찰)

  • Kim, Tae-Sik
    • Speech Sciences
    • /
    • v.10 no.2
    • /
    • pp.45-55
    • /
    • 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.

  • PDF

An Analysis Method of Strange Attractor for the Feature Extraction (음성 특징 추출을 위한 스트레인지 어트랙터의 분석 방법)

  • Kim, Tae-Sik
    • Speech Sciences
    • /
    • v.9 no.2
    • /
    • pp.147-155
    • /
    • 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.

  • PDF

A Study on the Enhancement of Ultrasonic Signal Recognition in Ferrite Carbon Steel Weld Zone Using Neural Networks (신경회로망을 이용한 페라이트계 탄소강 용접부의 초음파 신호 인식 향상에 관한 연구)

  • Yun, In-Sik;Park, Won-Kyou;Yi, Won
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.19 no.1
    • /
    • pp.158-164
    • /
    • 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.

Behavior of Multiple-Attractor Cellular Automata

  • Cho, Sung-Jin;Kim, Han-Doo;Ko, Gwi-Ja
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
    • /
    • /
    • pp.711-714
    • /
    • 2001
  • We present a detailed analysis of the behavior of a multiple-attractor cellular automata.

  • PDF