• Journal of Korea Water Resources Association
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• v.35 no.6
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• pp.817-826
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• 2002

Many researchers have been tried to forecast the future as analyzing data characteristics and the forecasting methodology may be divided into two cases of deterministic and stochastic techniques. However, the understanding data characteristics may be very important for model construction and forecasting. In the sense of this view, recently, the deterministic method known as nonlinear dynamics has been studied in many fields. This study uses the geometrical methodology suggested by Poincare for analyzing nonlinear dynamic systems and we apply the methodology to understand the characteristics of known systems and hydrologic data, and determines the possibility of forecasting according to the data characteristics. Say, we try to understand the data characteristics as constructing Poincare map by using Poincare section and could conjecture that the data sets are linear or nonlinear and an appropriate model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.1
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• pp.170-180
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• 1986

본 연구에서는 2자유도 Hamiltonian 운동계에서 비선형 정규모우드(normal mode)들의 안정성을 예측하기 위한 제3의 운동상수를 선형계의 진동수비가 1:1이고 포텐셜이 4차항까지 우함수인 일반계에 적용하여 발전시켰다. 이는 Hamiltonian을 정규모우드로 바꾸는 B-G변환과 함수들을 부호처리함과 Poincare map을 이용하다. 비선형계에서 비선형상수에 따라 모우드가 bifurcate되며, 각각의 모우드 안정성은 제3의 운동상수와 Poincare map으로 정확히 판정할 수 있다는 결론을 얻었다.

• Journal of KSNVE
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• v.9 no.1
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• pp.196-205
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• 1999

The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

• Journal of the Korean Society of Safety
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• v.14 no.4
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• pp.3-12
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• 1999

This research concentrates on the influence of non-linearities associated with impact for the nonlinear rocking behavior of rigid block subjected to one dimensional sinusoidal excitation of horizontal direction. The transition of two governing rocking equations, the abrupt reduction in the kinetic energy associated with impact, and sliding motion of block. In this study, two type of rocking vibration system are considered. One is the undamped rocking vibration system, disregarding energy dissipation at impact and the other is the damped rocking system, including energy dissipation and sliding motion. The response analysis using non-dimensional rocking equation is carried out for the change of excitation parameters and friction coefficient. The chaos responses were discovered in the wide response region, particularly, for the case of high excitation amplitude and their chaos characteristics were examined by the time history, Poincare map, power spectra and Lyapunov Exponent of rocking responses. The complex behavior of chaos response, in the phase space, were illustrated by Poincare map. The bifurcation diagram and Poincare map were shown to be effective in order to understand chaos of rocking system.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1922-1927
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• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• Journal of Theoretical and Applied Mechanics
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• v.1 no.1
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• pp.29-67
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• 1995

A procedure is formulated, in this paper, to compute the bifurcation modes born by the stability change of normal modes, and to compute the forced responses associated with bifurcation modes in inertially and elastically coupled nonlinear oscillators. It is assumed that a saddle-loop is formed in Poincare map at the stability chage of normal modes. In order to test the validity of procedure, it is applied to one-to-one internal resonant systems in which the solutions are guaranteed within the order of a small perturbation parameter. The procedure is also applied to the exact system in which normal modes are written in exact form and the stability of normal modes can be exactly determined. In this system the stability change of normal modes occurs several times so that various types of bifurcation modes are created. A method is described to identify a fixed point on Poincare map as one of bifurcation modes. The limitations and advantage of proposed procedure are discussed.

• Computational Structural Engineering
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• v.10 no.4
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• pp.239-249
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• 1997

The method to distinguish chaotic attractors in the perturbed response behaviors of a piecewise-linear system under combined regular and external randomness is provided and examined. In the noisy fields such as the ocean environment, excitation forces induced by wind, waves and currents contain a finite degree of randomness. Under external random perturbations, the system responses are disturbed, and consequently chaotic signatures in the response attractors are not distinguishable, but rather look just random-like. Mean Poincare map can be utilized to identify such chaotic responses veiled due to the random noise by averaging the noise effect out of the perturbed responses. In this study, the procedure to create mean Poincare map combined with the direct numerical simulations is provided and examined. It is found that mean Poincare maps can successfully distinguish chaotic attractors under stochastic excitations, and also can give the information of limit value of noise intensity with which the chaos signature in system responses vanishes.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.1
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• pp.113-119
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• 2013

In this paper, n order to degrade of diagnosis of power supply by using Poincare map and fractal dimension with temperature measured by infrared camera. we review the characteristic of temperature variation according to pattern variation of power supply in chemical industry complex. As a simulation results we can be realized the characteristic behaviors of nonlinear dynamics in the poincare mal and fractal dimension. In the future verification method requires through additional research.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.295-300
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• 1996

In this study, the dynamic instabilities of a nonlinear elastic system subjected to follower force are investigated. The two-degree-of-freedom double pendulum model with nonlinear geometry, cubic spring, and linear viscous damping is used for the study. The constant and periodic follower forces are considered. The chaotic nature of the system is identified using the standard methods, such as time histories, phase portraits, and Poincare maps, etc.. The responses are chaotic and unpredictable due to the sensitivity to initial conditions. The sensitivities to parameters, such as geometric initial imperfections, magnitude of follower force, and viscous damping, etc. is analysed. The strange attractors in Poincare map have the self-similar fractal geometry. Dynamic buckling loads are computed for various parameters, where the loads are changed drastically for the small change of parameters.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.9C
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• pp.860-867
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• 2003

In this paper, an efficient core point detection method using orientation pattern labeling is proposed in fingerprint image. The core point, which is one of the singular points in fingerprint image, is used as the reference point in the most fingerprint recognizing system. Therefore, the detection of the core point is the most essential step of the fingerprint recognizing system, it can affect in the whole system performance. The proposed method could detect the position of the core point by applying the labeling method for the directional pattern which is come from the distribution of the ridges in fingerprint image and applying detailed algorithms for the decision of the core point's position. The simulation result of proposed method is better than the result of Poincare index method and the sine map method in executing time and detecting rate. Especially, the Poincare index method can't detect the core point in the detection of the arch type and the sine map method takes too much times for executing. But the proposed method can overcome these problems.