• East Asian mathematical journal
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• 제31권5호
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• pp.743-751
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• 2015

In this paper, we consider a discrete ratio-dependent predator-prey system with harvesting effect. In order to investigate dynamical behaviors of this system, first we find out all fixed points of the system and then classify their stabilities by using their Jacobian matrices and local stability method. Next, we display some numerical examples to substantiate theoretical results and finally, we show numerically, by means of a bifurcation diagram, that various dynamical behaviors including cycles, periodic doubling bifurcation and chaotic bands can be existed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.270-275
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• 2003

The nonlinear dynamic characteristic of a straight tube conveying fluid with constraints and an attached mass on the tube is examined in this study. An experimental apparatus composed of an elastomer tube conveying water which has an attached mass and constraints is made and comparisons are done between the theoretical results from non-linear equation of motion of piping system and experimental results. And the results show that the tube is destabilized as the mass of the attached mass increases, and stabilized as the position of the attached mass close to the fixed end. In case of a small end-mass, the system shows rich and different types of periodic solutions. For a constant end-mass, the system undergoes a series of bifurcations after the first Hopf bifurcation, as the flow velocity increases, which causes chaotic motion of the tube eventually.

• 한국소음진동공학회논문집
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• 제14권7호
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• pp.561-568
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• 2004

The nonlinear dynamic characteristic of a straight tube conveying fluid with constraints and an attached mass on the tube is examined in this study An experimental apparatus with an elastomer tube conveying water which has an attached mass and constraints is made and comparisons are made between the theoretical results from the non-linear equation of motion of piping system and the experimental results. The comparisons show that the tube is destabilized as the magnitude of the attached mass increases, and stabilized as the position of the attached mass closes to the fixed end. In case of a small end-mass, the system shows complicated and different types of solutions. For a constant end-mass. the system undergoes a series of bifurcations after the first Hopf bifurcation, as the flow velocity increases. which causes chaotic motions of the tube eventually.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2007년도 춘계학술대회 논문집
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• pp.258-261
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• 2007

Failure phenomena in uni-axial tension test were experimentally and numerically investigated for AA6111-T4, AA5083-H18 and DP-Steel, which were friction-stir welded with the same and different thicknesses. Forming limit diagram(FLD) was measured using hemispherical dome stretching tests for base materials and also predicted by Hill's bifurcation and M-K theories for welded areas. Finite element simulations well predicted hardening behaviors, failure locations as well as failure patterns for the uni-axial tension tests especially utilizing very fine meshes and FLD along with stress softening.

• 대한조선학회논문집
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• 제36권3호
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• pp.71-82
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• 1999

비선형 동역학계의 불규칙한 운동은 그 계가 가지는 고유한 특성에 의해 생기는 현상으로써 때로는 예측할 수 없는 큰 운동이 발생한다. 해상 운행중인 선박의 경우 이러한 예측치 못한 큰 운동으로 인해 전복이 일어나기도 하므로, 비선형 선박 안전성 확보라는 관점에서 중요하게 다루어져야 한다. 본 연구에서는, 첫째로 임의의 구간 안에 있는 모든 초기 조건에 대해 선박 운동의 안정성을 파악하여 안정과 불안정으로 영역 구분을 시켜 주는 흡인 영역(basins of attraction)을 외력변화에 따라 그려 봄으로써 선박 운동에 대한 안정 영역의 정성적인 변화 과정을 파악하고자 하였다. 둘째로 전복이 일어나지 않는 안정 영역상을 초기 조건으로 한 선박 운동이 최종적으로 어떤 운동이 되는지 알아 보았다. 마지막으로 외력 변화에 따른 비선형 선박 운동 중 혼돈적 현상이 일어나는 운동에 대해서는 이를 상세히 분석하고자 과도상태가 지난 운동의 주기적 변화를 외력 변화에 따라 살펴보는 분기도(bifurcation diagram)를 이용하여 연구해 보았다.

• 소성∙가공
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• 제16권4호
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• pp.304-308
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• 2007

Failure phenomena in uni-axial tension test were experimentally and numerically investigated for AA6111-T4, AA5083-H18 and DP-Steel, which were friction-stir welded with the same and different thicknesses. Forming limit diagram(FLD) was measured using hemispherical dome stretching tests for base materials and also predicted by Hill's bifurcation and M-K theories for welded areas. Finite element simulations well predicted hardening behaviors, failure locations as well as failure patterns for the uni-axial tension tests especially utilizing very fine meshes and FLD along with stress softening.

• 대한수학회지
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• 제46권2호
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• pp.363-447
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• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1999년도 추계종합학술대회 논문집
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• pp.693-696
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• 1999

This paper presents an analysis of the chaotic behavior in the discrete-time chaotic generator fabricated by CMOS technology. An approximated empirical equation is extracted from the measurement data of a nonlinear function block. Then the bifurcation diagram and Lyapunov exponent and time waveforms and frequency responses of the chaotic generator are calculated and simulated. And results of experiments in the chaotic circuit with the $\pm$2.5V power supply and clock rate of 10KHz are shown, and analysed.

• Journal of Electrical Engineering and Technology
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• 제2권3호
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• pp.300-305
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• 2007

This paper reports an investigation of overvoltages caused by ferroresonance in the distribution system, which consists of a bank of open-delta single-phase voltage transformers. The high voltage sides of the voltage transformer are connected to the distribution system via three single-phase fuse cutouts. Due to the saturation characteristic of the transformer cores, ferroresonance can occur in the condition that the transformer is energized or deenergized with single-phase switching operation of the fuse cutouts. The simulation tool based on EMTP is used to investigate the overvoltages at the high side of voltage transformer. Bifurcation diagrams are used to present the ferroresonance behavior in ranges of different operating conditions. The simulation results are in good agreement with the results from the experiment of 22 kV voltage transformers. The mitigation technique with additional damping resistors in the secondary windings of the voltage transformers will be introduced. Brief discussion will be made on the physical phenomena related to the overvoltage and the damage of voltage transformer.

• 한국통신학회논문지
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• 제22권2호
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• pp.318-324
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• 1997

Chua 회로는 간단한 전기 및 전자 회로를 구성하여 카오스 현상을 나타내는 회로로 자율, 3차계, 가역성(Reciprocal)이며 1개의 비션형 소자인 3구분 선형 저항과 4개의 선형 소자인 (R, L, $C_1,\;C_2$)로 구성되는 발진회로이다. 본 논문에서는 Chua 회로의 병렬 LC 공진기를 단락하여 시간 지연을 갖는 무손실 전송선로로 치환하고 특성 곡선법을 써서 파라미터 변화에 의한 카오스 운동과 주기운동이 있음을 위상공간과 분기도(Bifurcation diagram)로 확인 하였으며 무손실 전송선로가 원래의 Chua 회로와 유사한 어트렉터가 존재함을 확인하였다.