• Korean Journal of Mathematics
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• v.26 no.2
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• pp.327-335
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• 2018

In this paper, we present the construction of natural invariant measures so called SRB(Sinai-Ruelle-Bowen) measures by the properties of geometric t-potential and Bowen's equation for the hyperbolic attractors.

• The Journal of the Korea institute of electronic communication sciences
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• v.10 no.5
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• pp.593-598
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• 2015

Non-linear cellular automata is difficult to analyze mathematically than linear cellular automata. So it is difficult to identify reachable states and attractors of nongroup non-linear cellular automata than nongroup linear cellular automata. In this paper, we propose a new reachable table to overcome these problems. We can see the next state for all the states of the non-linear cellular automata by the proposed reachable table. In addition, we can identify reachable states and attractors by the reachable table.

• Smart Structures and Systems
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• v.11 no.1
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• pp.87-102
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• 2013

Vibration-based damage detection methods are popular for structural health monitoring. However, they can only detect fairly large damages. Usually impact pulse, ambient vibrations and sine-wave forces are applied as the excitations. In this paper, we propose the method to use the chaotic excitation to vibrate structures. The attractors built from the output responses are used for the minor damage detection. After the damage is detected, it is further quantified using the Kalman Filter. Simulations are conducted. A 5-story building is subjected to chaotic excitation. The structural responses and related attractors are analyzed. The results show that the attractor distances increase monotonously with the increase of the damage degree. Therefore, damages, including minor damages, can be effectively detected using the proposed approach. With the Kalman Filter, damage which has the stiffness decrease of about 5% or lower can be quantified. The proposed approach will be helpful for detecting and evaluating minor damages at the early stage.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.2
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• pp.318-324
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• 1997

Chua's circuit is a simple electronic network which exhibits a variety of bifurcation and attractors. The circuit consists of two capacitors, a linear resistor, and a nonlinear resistor. In this papre we analyze a circuit obtained by replacing the parallel LC resonator in the Chua's circuit by lossless transmission line. By using the method of characteristics of this circuit we show that various periodic motions and chaotic motions can the attained according to parameter variations. From Chua's circuit with a lossless transmission line a variely of chaotic attractors which are similar to those of the normal Chua's circuit are observed.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.3
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• pp.71-82
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• 1999

Irregular motions of nonlinear dynamic system are the result of an intrinsic characteristics that the system have, and sometimes occur unpredictable large motion. For a ship in a regular seaway, the capsizing occur because of this unexpectable motion. So, from the safety's point of view, nonlinear ship motions should be treated carefully. In this study, stable and unstable regions are investigated firstly under the variation of a control external force. Secondly, we consider the attractors to know how ship motions of the stable region that does not undergo capsizing change. Thirdly, bifurcation diagram is considered to study the range in detail where nonlinear chaotic motions are occurred.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.631-638
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.143-159
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• 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.

• Journal of Advanced Marine Engineering and Technology
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• v.21 no.1
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• pp.71-81
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• 1997

This paper describes an implementation of Chua's oscillator circuits with five - segment piecewise -linear function. Some bifurcation phenomena and chaotic attractors observed experimentally from the laboratory model and simulated by computer for the model are also presented. The Chua's oscillator circuit is implemented with analog electronic devices. Com¬paring both the observations and simulations, the spectrums are satisfactory.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.927-933
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• 2020

We characterize Möbius functions mapping the unit disc of the complex plane contractively into itself. We then give a procedure to produce Möbius iterated function systems on the unit disc.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.457-462
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• 1996

Recently Hurley [3] proved that if A is a weak attractor of a discrete dyanamical system f then there exists a Lyapunov-like function for A. The purpose of this note is to study whether the converse of the above result does hold or not.