• 전력전자학회:학술대회논문집
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• 전력전자학회 1999년도 전력전자학술대회 논문집
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• pp.650-654
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• 1999

In this paper, author describe the simulation results concerning the period doubling bifurcation route to chaos of DC/DC boost converter under current mode control to show that it is common phenomena on switching regulator when parameters are improperly chosen or continuously varied beyond the ensured region by system designer. Bifurcation diagrams of periodic orbits of inductor current and capacitor voltage of DC/DC boost converter are plotted with sampled data at moment of each clock pulse causing switching on. DC/DC boost converter studied on this paper is modelled by its state space equations as per switching condition under continuous conduction mode. Current reference signal and capacitance are chosen as the bifurcation parameters and those are varied in step for iterative calculation to find bifurcation points of periodic orbits of state variables.

• KIEE International Transactions on Power Engineering
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• 제4A권1호
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• pp.1-5
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• 2004

The model of a power system with load dynamics is studied by investigating qualitative changes in its behavior as the reactive power demand at a load bus is increased. The load is created using induction motors parallel with the constant power and constant impedance load. As the load increases, the system experiences various bifurcations such as sub critical and supercritical Hopf, period-doubling and saddle-node bifurcation. The latter may lead the system to voltage collapse. A nonlinear controller is used to control the subcritical Hopf bifurcation and hence mitigate voltage collapse. It is applied to the KEPCO (Korean Electric Power Company) system to demonstrate its validity.

• 한국연소학회지
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• 제17권3호
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• pp.9-16
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• 2012

Nonlinear dynamics of pulsating instability in radiating counterflow diffusion flames is numerically investigated by imposing Damk$\ddot{o}$hler number perturbation. Stable limit-cycle solutions occur in small ranges of Damk$\ddot{o}$hler numbers past bifurcation point of instability. Period doubling cascade and chaotic behaviors appear just before dynamic extinction occurs. Nonlinear dynamics is also studied when large disturbances are imposed to flames. For weak steady flames, the dynamic extinction range shrinks as the magnitudes of disturbances are increased. However, strong steady flames can overcome relatively large disturbances, thereby the dynamic extinction range extending. Stable limit-cycle behaviors reappears prior to dynamic extinction when the steady flames are strong enough.

• 한국소음진동공학회논문집
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• 제13권4호
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• pp.317-322
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• 2003

Torsional oscillations of a system incorporating a Hooke's joint are investigated by adopting a nonlinear 2-degree-of-freedom model. Linear and Van der Pol transformations are applied to obtain the equations of motion to which the method of averaging can be readily applied. Various subharmonic and combination resonances are identified with the conditions of their occurrences. Applying the method of averaging leads to the reduced amplitude- and phase-equations of motion, of which constant and periodic solutions are obtained numerically. The periodic solution which emerges from Hopf bifurcation point experiences period doubling bifurcation leading to infinite solution rather than chaotic solution.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.430-435
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• 2005

조화가진력이 작용하는 고정경계를 가진 완전원판의 비선형 진동에 대한 응답특성을 연구하였다. 원판의 비대칭모드의 고유진동수 근처에 가진주파수가 작용하는 주공진에서의 응답은 정상파(standing wave)뿐만 아니라 진행파(traveling wave)가 존재한다고 알려져 있다. 주공진 근처의 정상상태 응답곡선에서 최대한 5개의 안정한 응답이 존재하는 것으로 밝혀졌으며, 이들은 1개의 정상파와 4개의 진행파로 나타난다. 이 진행파중 2개는 Hope분기에 의해 안정성을 잃은 후 주기배가운동을 거쳐 혼돈운동에 이르게 된다. Lyaponov 지수를 사용하여 혼돈운동을 정량적으로 평가하였으며, 주평면의 개념을 이용하여 이 혼돈운동의 흡인영역이 Fractal임을 확인하였다.

• 한국소음진동공학회논문집
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• 제21권9호
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• pp.813-819
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• 2011

This paper predicted nonlinear dynamic responses of a cantilevered carbon nanotube(CNT) resonator incorporating the electrostatic forces and van der Waals interactions between the CNT cantilever and ground plane. The structural model of CNT includes geometric and inertial nonlinearities to investigate various phenomena of nonlinear responses of the CNT due to the electrostatic excitation. In order to solve this problem, we used Galerkin's approximation and the numerical integration techniques. As a result, the CNT nano-resonator shows the softening effect through saddle-node bifurcation near primary resonance frequency with increasing the applied AC and DC voltages. Also we can predict nonlinear secondary resonances such as superharmonic and subharmonic resonances. The superharmonic resonance of the nano-resonator is influenced by applied AC voltage. The period-doubling bifurcation leads to the subharmonic resonance which occurs when the nano-resonator is actuated by electrostatic forces as parametric excitation.

• 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.

• KIEE International Transactions on Power Engineering
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• 제4A권1호
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• pp.18-25
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• 2004

This paper proposes a totally new method in the chaos characteristics' analysis of power systems, the introduction of topological invariants. Using a return histogram, a bifurcation graph was drawn. As well, the periodic orbits and topological invariants - the local crossing number, relative rotation rates, and linking number during the process of period-doubling bifurcation and chaos were extracted. This study also examined the effect on the topological invariants when the sensitive parameters were varied. In addition, the topological invariants of a three-dimensional embedding of a strange attractor were extracted and the result was compared with those obtained from differential equations. This could be a new approach to state detection and fault diagnosis in dynamical systems.

• 한국진공학회지
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• 제21권5호
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• pp.249-257
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• 2012

1차원 유체 모델을 사용하는 수치 코드를 개발하여 Pierce 다이오드에서 플라즈마에 대한 비선형 동력학적 거동을 연구하였다. Pierce 다이오드에서 플라즈마는 전극에서 방출되는 전자 전류와 전극 사이의 거리로 결정되는 Pierce 매개 변수가 변화함에 따라 안정하기도 하고 불안정해지기도 한다. 중성 및 비중성 Pierce 시스템의 동력학적 특성에 대해 해석적 및 수치적으로 연구하였다. Pierce 매개 변수의 값에 따라 플라즈마는 증폭 모드 또는 진동 모드를 가질 수 있으며, 진동 모드에서는 매개 변수가 감소함에 따라 계속적인 주기 배가 쌍갈림(period doubling bifurcation)을 일으키며 카오스 상태에 도달하게 된다. 이러한 거동에 대한 분석은 보다 복잡한 구조에서의 빔-플라즈마 상호작용에 대한 기본적인 이해를 위한 모델 및 카오스 제어를 위한 자료로서 사용될 수 있다.

• Wind and Structures
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• 제7권4호
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• pp.265-280
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• 2004

This paper presents some fundamental results on the dynamics of the periodic Karman wake behind a circular cylinder. The wake is treated like a dynamical system. External forcing is then introduced and its effect investigated. The main result obtained is the following. Perturbation of the wake, by controlled cylinder oscillations in the flow direction at a frequency equal to the Karman vortex shedding frequency, leads to instability of the Karman vortex structure. The resulting wake structure oscillates at half the original Karman vortex shedding frequency. For higher frequency excitation the primary pattern involves symmetry breaking of the initially shed symmetric vortex pairs. The Karman shedding phenomenon can be modeled by a nonlinear oscillator. The symmetrical flow perturbations resulting from the periodic cylinder excitation can also be similarly represented by a nonlinear oscillator. The oscillators represent two flow modes. By considering these two nonlinear oscillators, one having inline shedding symmetry and the other having the Karman wake spatio-temporal symmetry, the possible symmetries of subsequent flow perturbations resulting from the modal interaction are determined. A theoretical analysis based on symmetry (group) theory is presented. The analysis confirms the occurrence of a period-doubling instability, which is responsible for the frequency halving phenomenon observed in the experiments. Finally it is remarked that the present findings have important implications for vortex shedding control. Perturbations in the inflow direction introduce 'control' of the Karman wake by inducing a bifurcation which forces the transfer of energy to a lower frequency which is far from the original Karman frequency.