• Journal of Mechanical Science and Technology
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• v.16 no.9
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• pp.1040-1053
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• 2002

This research deals with the influence of nonlinearities associated with impact and sliding upon the rocking behavior of a rigid block, which is subjected to two-dimensional horizontal and vertical excitation. Nonlinearities in the vibration were found to depend strongly on the effect of the impact between the block and the base, which involves an abrupt reduction in the system's kinetic energy. In particular, when sliding occurs, the rocking behavior is substantially changed. Response analysis using a non-dimensional rocking equation was carried out for a variety of excitation levels and excitation frequencies. The chaos responses were observed over a wide response region, particularly, in the cases of high vertical displacement and violent sliding motion, and the chaos characteristics appear in the time histories, Poincare maps, power spectra and Lyapunov exponents of the rocking responses. The complex behavior of chaotic response, in phase space, is illustrated by the Poincare map. The distribution of the rocking response is described by bifurcation diagrams and the effects of sliding motion are examined through the several rocking response examples.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.1 no.1
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• pp.104-112
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• 2001

Simply, Nonlinear dynamics theory means the complicated and noise-like phenomena originated form nonlinearity involved in deterministic dynamical system. An almost all the natural signals have nonlinear property. However, there exist few analysis software tool or package for a research and development of applications. We develop nonlinear time series analysis simulator is to provide a common and useful tool for this purpose and to promote research and development of nonlinear dynamics theory. This simulator is consists of the following four modules such as generation module, preprocessing module, analysis module and ICA module. In this paper, we applied to Electroencephalograph (EEG), as it turned out, our simulator is able to analyze nonlinear time series. Besides, we could get the useful results using the various parameters. These results are used to diagnostic the brain diseases.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.537-547
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• 1995

Numerical study on the chaotic stirring of viscous flow in an alternately driven cavity has been performed. Even under the Stokes-flow assumption, the inherent singularity at the corners made the problem not so easily accessible. With some special treatments to the region near the corners, the biharmonic equation was solved numerically by using the fully implicit method. The velocity field was then used in obtaining the trajectories of passive particles for studying the stirring effect. The three tools developed in the field of the nonlinear dynamics and chaos, that are the Poincare sections, the unstable manifolds, and the Lyapunov exponents, were used in analysing the stirring effect. It was shown that the unstable manifolds obtained in this study well fit the experimental results given by the previous investigators. It is predicted that the best stirring can be obtained when the aspect ratio a is near 0.8 and the dimensionless period T is in the range 4.3 - 4.7.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.817-821
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• 1997

Ever since the nonlinearity of machine tool dynamics was established, researchers attempted to make use of this fact to devise better monitoring, diagnostics and system, which were hitherto based on linear models. Theory of chaos, which explains many nonlinear phenomena comes handy for furthering the analysis using nonlinear model. In this study, measuring system will be constructed using multi-sensor (Tool Dynamometer, Acoustic Emission) in end millingprocess. Then, it will be verified that cutting force is low-dimensional deterministic chaos calculating Lyapunov exponents, Fractal dimension, Embedding dimension. Aen it will be investigated that the relations between characteristic parameter caculated form sensor signal and tool wear.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.225-228
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• 1992

The purpose of this project is the presentation of new method for selection of a scalar control of linear time-periodic system. The approach has been proposed by Radziszewski and Zaleski [4] and utilizes the quadratic form of Lyapunov function. The system under consideration is assigned either in closed-loop state or in modal variables as in Calico, Wiesel [1]. The case of scalar control is considered, the gain matrix being assumed to be at worst periodic with the system period T, each element being represented by a Fourier series. As the optimal gain matrix we consider the matrix ensuring the minimum value of the larger real part of the two Poincare exponents of the system. The method, based on two-step optimization procedure, allows to find the approximate optimal gain matrix. At present state of art determination of the gain matrix for this case has been done by systematic numerical search procedure, at each step of which the Floquet solution must be found.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.11
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• pp.93-101
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• 1997

Ever since the nonlinearity of machine tool dynamics was established, researchers attempted to make use of this fact to devise better monitoring, diagnostics and control system, which were hitherto based on linear models. Theory of chaos which explains many nonlinear phenomena comes handy for furthering the analysis using nonlinear model. In this study, measuring system will be constructed using multi-sensor (Tool Dynamometer, Acoustic Emission) in end milling process. Then, it will be verified that cutting force is low-dimensional chaos by calculating Lyapunov exponents. Fractal dimension, embedding dimension. And it will be investigated that the relation between characteristic parameter calculated from sensor signal and tool wear.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.962-964
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• 1995

In this paper, an integrated chaos analysis system for EEG (ICASE) is designed for the analysis of brain functions based on the chaos theory. Nonlinear dynamic characteristics of EEG such as 3-D attractor, Poincare section, correlation dimension, Lyapunov exponents and power spectrum are extracted by this system. The results show that chaotic attractors which indicate the presence of deterministic, dynamics of complex nature could be identified from a routine EEG recording for normal and pathological activity. This proves that the chaotic analysis of EEG may be an appropriate tool in the classification of brain activity and thus a possible diagnostic tool.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.825-855
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• 2019

We establish the existence of $C^1$ stable invariant manifolds for differential equations $u^{\prime}=A(t)u+f(t,u,{\lambda})$ obtained from sufficiently small $C^1$ perturbations of a nonuniform exponential dichotomy. Since any linear equation with nonzero Lyapunov exponents has a nonuniform exponential dichotomy, this is a very general assumption. We also establish the $C^1$ dependence of the stable manifolds on the parameter ${\lambda}$. We emphasize that our results are optimal, in the sense that the invariant manifolds are as regular as the vector field. We use the fiber contraction principle to establish the smoothness of the invariant manifolds. In addition, we can also consider linear perturbations, and thus our results can be readily applied to the robustness problem of nonuniform exponential dichotomies.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.547-562
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• 2024

By utilizing coupling the strategy in the 5D Sprott B system, a new no equilibrium 7D hyperchaotic system is introduced. Despite the proposed system being simple with twelve-term, including solely two cross product nonlinearities, it displays extremely rich dynamical features such as hidden attractors and the dissipative and conservative nature. Besides, this system has largest Kaplan-Yorke dimension compared with to the work available in the literature. The dynamical properties are fully investigated via Matlab 2021 software from several aspects of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, offset boosting and so on. Moreover, the corresponding circuit is done through Multisim 14.2 software and preform to verify the new 7D system. The numerical simulations wit carryout via both software are agreement which indicates the efficiency of the proposed system.