• 대한전기학회:학술대회논문집
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• 대한전기학회 1995년도 하계학술대회 논문집 B
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• pp.664-666
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• 1995

Chua's circuit is a simple electronic network which exhibits a variety of bifurcation and attractors. The circuit consists of two capacitors, an inductor, a linear resistor and a nonlinear resistor. This paper describes the implementation for a practical op amp of Chua's circuit. In experiment results, 1 periodic motion, 2 periodic motion, rossler type attractors, stranger chaotic attractor periodic window and limit cycle are shown, which are coincide with computer simulation.

• Korean Journal of Mathematics
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• 제22권4호
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• pp.621-632
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• 2014

In this paper, we study the dynamical behavior of the one-dimensional convective Cahn-Hilliard equation(CCHE) on a periodic cell [$-{\pi},{\pi}$]. We prove that as the control parameter passes through the critical number, the CCHE bifurcates from the trivial solution to an attractor. We describe the bifurcated attractor in detail which gives the final patterns of solutions near the trivial solution.

• 한국항공운항학회지
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• 제21권4호
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• pp.47-52
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• 2013

In this paper, limit cycle flutter induced by Hopf bifurcation is studied with nonlinear system analysis approach and observed for the critical slowing down phenomenon. Considering an attractor of the dynamics of a system, when a small perturbation is applied to the system, the dynamics converge toward the attractor at some rate. The critical slowing down means that this recovery rate approaches zero as a parameter of the system varies and the size of the basin of attraction shrinks to nil. Consequently, in the pre-bifurcation regime, the recovery rates decrease as the system approaches the bifurcation. This phenomenon is one of the features used to forecast bifurcation before they actually occur. Therefore, studying the critical slowing down for limit cycle flutter behavior would have potential applicability for forecasting those types of flutter. Herein, modeling and nonlinear system analysis of the 2D airfoil with torsional nonlinearity have been discussed, followed by observation of the critical slowing down phenomenon.

• 대한수학회보
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• 제49권5호
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• pp.923-937
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• 2012

In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic cell ${\Omega}=[-L,L]$. It is shown that the equations bifurcates from the trivial solution to an attractor $\mathcal{A}_{\lambda}$ when th control parameter ${\lambda}$ crosses the critical value. In the odd periodic case $\mathcal{A}_{\lambda}$ is homeomorphic to $S^1$ and consists of eight singular points and thei connecting orbits. In the periodic case, $\mathcal{A}_{\lambda}$ is homeomorphic to $S^1$, an contains a torus and two circles which consist of singular points.

• 대한수학회보
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• 제52권4호
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• pp.1241-1252
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• 2015

In this paper, we study the dynamical bifurcation of the modified Swift-Hohenberg equation on a periodic interval as the system control parameter crosses through a critical number. This critical number depends on the period. We show that there happens the pitchfork bifurcation under the spatially even periodic condition. We also prove that in the general periodic condition the equation bifurcates to an attractor which is homeomorphic to a circle and consists of steady states solutions.

• Journal of Advanced Marine Engineering and Technology
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• 제22권6호
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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.

• Journal of Advanced Marine Engineering and Technology
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• 제21권1호
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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.

• 소음진동
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• 제7권3호
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• pp.489-498
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• 1997

In this paper, chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonliear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which has the external and parametric excitation with a same frequency. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Numerical simulations are performed to demonstrate theoretical results and show the strange attractor of the chaotic motion.

• Structural Engineering and Mechanics
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• 제51권5호
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• pp.743-754
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• 2014

Investigations of regular and chaotic vibrations of the autoparametric pendulum absorber suspended on a nonlinear coil spring and a magnetorheological damper are presented in the paper. Application of a semi-active damper allows controlling the dangerous motion without stooping of system and additionally gives new possibilities for designers. The investigations are curried out close to the main parametric resonance. Obtained numerical and experimental results show that the semi-active suspension may reduce dangerous motion and it also allows to maintain the pendulum at a given attractor or to jump to another one. Moreover, the results show that, for some parameters, MR damping may transit to chaotic motions.

• 대한수학회지
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• 제48권6호
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• pp.1101-1123
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• 2011

Numerical schemes are routinely used to predict the behavior of continuous dynamical systems. All such schemes transform flows into maps, which can possess dynamical behavior deviating from their continuous counterparts. Here the common bifurcations of scalar dynamical systems are transformed under a class of algorithms known as linearized one-point collocation methods. Through the use of normal forms, we prove that each such bifurcation in an originating flow gives rise to an exactly corresponding one in its discretization. The conditions for spurious period doubling behavior under this class of algorithm are derived. We discuss the global behavioral consequences of a singular set induced by the discretizing methods, including loss of monotonicity of solutions, intermittency, and distortion of attractor basins.