• Title, Summary, Keyword: attractor

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Spectrums of Chua's Oscillator Circuit with a Cubic Nonlinear Resistor (Cubic 비선형 저항에 의한 카오스 발진회로의 스펙트럼)

  • 김남호
    • Journal of Advanced Marine Engineering and Technology
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    • v.22 no.6
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    • pp.908-919
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    • 1998
  • This paper describes implementation and simulation of Chua's oscillator circuits with a cubic non-linear resistor. The two-terminal nonlinear resistor NR consists of one Op Amp two multipliers and five resistors. The Chua's oscillator circuit is implemented with analog electronic devices. Period-1 limit cycle period-2 limit cycle period-4 limit cycle and spiral attractor double-scroll attractor and 2-2 window are observed experimentally from the laboratory model and simulated by computer for the presented model. Comparing the result of experiments and simulations the spectrums are satisfied.

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UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS GENERALIZED 2D PARABOLIC EQUATIONS

  • PARK, JONG YEOUL;PARK, SUN-HYE
    • Journal of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.1149-1159
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    • 2015
  • This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $$-{\Delta}u_t+{\alpha}^2{\Delta}^2u_t+{\mu}{\Delta}^2u+{\bigtriangledown}{\cdot}{\vec{F}}(u)+B(u,u)={\epsilon}g(x,t)$$. Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor $\{A_{\epsilon}(t)\}_{t{\epsilon}{\mathbb{R}}}$ of the equation with ${\epsilon}>0$ converges to the global attractor A of the equation with ${\epsilon}=0$.

EXISTENCE AND LONG-TIME BEHAVIOR OF SOLUTIONS TO NAVIER-STOKES-VOIGT EQUATIONS WITH INFINITE DELAY

  • Anh, Cung The;Thanh, Dang Thi Phuong
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.379-403
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    • 2018
  • In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

Verification on Chaotic Behavior of Cutting Force in Metal Cutting (절삭가공시 절삭력 신호의 카오스적거동에 관한 규명)

  • 구세진
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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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.

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Nonlinear Time Series Analysis of Biological Chaos (생체 카오스의 비선형 시계열 데이터 분석)

  • 이병채;이명호
    • 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.

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THE CONE PROPERTY FOR A CLASS OF PARABOLIC EQUATIONS

  • KWAK, MINKYU;LKHAGVASUREN, BATAA
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.21 no.2
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    • pp.81-87
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    • 2017
  • In this note, we show that the cone property is satisfied for a class of dissipative equations of the form $u_t={\Delta}u+f(x,u,{\nabla}u)$ in a domain ${\Omega}{\subset}{\mathbb{R}}^2$ under the so called exactness condition for the nonlinear term. From this, we see that the global attractor is represented as a Lipshitz graph over a finite dimensional eigenspace.

ALGORITHM FOR THE CONSTRUCTION OF THE STATE TRANSITION DIAGRAM OF A SACA OVER GF($2^p$)

  • Choi, Un-Sook;Cho, Sung-Jin
    • 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.

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GLOBAL ATTRACTOR OF THE WEAKLY DAMPED WAVE EQUATION WITH NONLINEAR BOUNDARY CONDITIONS

  • Zhu, Chaosheng
    • 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.

Extraction of Speaker Recognition Parameter Using Chaos Dimension (카오스차원에 의한 화자식별 파라미터 추출)

  • Yoo, Byong-Wook;Kim, Chang-Seok
    • 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.

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BOUNDS OF CORRELATION DIMENSIONS FOR SNAPSHOT ATTRACTORS

  • Chang, Sung-Kag;Lee, Mi-Ryeong;Lee, Hung-Hwan
    • 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 ${\iota}\;{\geq}\;1$.