• Journal of Mechanical Science and Technology
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• 제17권9호
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• pp.1249-1260
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• 2003

This present work focuses on the influence of nonlinearities associated with impact on the rocking behavior of a rigid body block subjected to a two-dimensional excitation in the horizontal and vertical directions. The nonlinearities in rocking system are found to be strongly dependent on the impact between the block and the base that abruptly reduces the kinetic energy. In this study, the rocking systems of the two types are considered : The first is an undamped rocking system model that disregards the energy dissipation during the impact and the second is a damped rocking system, which incorporates energy dissipation during the impact. The response analysis is carried out by a numerical method using a non-dimensional rocking equation in which the variations in the excitation levels are considered. Chaos responses are observed over a wide range of parameter values, and particularly in the case of large vertical displacements, the chaotic characteristics are observed in the time histories, Poincare sections, the power spectral density and the largest Lyapunov exponents of the rocking responses. Complex behavior characteristics of rocking responses are illustrated by the Poincare sections.

• 대한기계학회논문집
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• 제18권2호
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• pp.380-388
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• 1994

Study on the chaotic stirring has been performed numerically and experimentally for a shallow rectangular tank accompanying a vortex shedding. The model is composed of a rectangular tank with a vertical plate with a length half the width of the tank. The tank is subject to a horizontal sinusoidal oscillation. The chaotic stirring was analysed by Poincare sections, unstable manifolds and Lyapunov exponents. As Reynolds number is increased the stirring effect is decreased due to the growth of a regular regions near the lower surface of the tank. In the other hand decrease of Reynolds number gives a weaker vortex shedding resulting in the poorer stirring effect. It was also found that the Lyapunov exponent is the highest at the dimensionless period of 1.3-1.5, which seems to be the best condition for the efficient stirring. The experimental visualization for the deformation of materials exhibits the striation pattern similar to the unstable manifold obtained numerically.

• 한국정밀공학회지
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• 제15권12호
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• pp.226-235
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• 1998

This study proposes the analysis and evaluation of method of time series of ultrasonic signal using the chaotic feature extraction for ultrasonic pattern recognition. The features are extracted from time series data for analysis of weld defects quantitatively. For this purpose, analysis objectives in this study are fractal dimension, Lyapunov exponent, and strange attractor on hyperspace. The Lyapunov exponent is a measure of rate in which phase space diverges nearby trajectories. Chaotic trajectories have at least one positive Lyapunov exponent, and the fractal dimension appears as a metric space such as the phase space trajectory of a dynamical system. In experiment, fractal(correlation) dimensions and Lyapunov exponents show the mean value of 4.663, and 0.093 relatively in case of learning, while the mean value of 4.926, and 0.090 in case of testing in slag inclusion(weld defects) are shown. Therefore, the proposed chaotic feature extraction can be enhancement of precision rate for ultrasonic pattern recognition in defecting signals of weld zone, such as slag inclusion.

• 한국지능정보시스템학회:학술대회논문집
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• 한국지능정보시스템학회 2001년도 The Pacific Aisan Confrence On Intelligent Systems 2001
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• pp.111-115
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• 2001

In this paper, a simple and systematic control design method is proposed for a discrete-time Takagi-Sugeno(TS) fuzzy system, which employs the parallel distributed compensation(PDC) to determine the structure of a fuzzy controller so as to mark all the Lyaunov exponents of the controlled TS fuzzy system strictly positive. This approach is proven to be mathematically rigorous for anticontrol of chaos for a TS fuzzy system in the sense that any given discrete-time TS fuzzy system can be made chaotic by the designed PDC controller along with the-operation. A numerical example is included to visualize the anticontrol effect.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1995년도 춘계학술대회논문집; 전남대학교, 19 May 1995
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• pp.121-128
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• 1995

The results are summarized as what follows: 1) The modeling of thin beams, which is a continuous system, into a two DOF system yields satisfactory results for the chaotic vibrations. 2) The concept of "natural forcing function" derived from the eigenfunction of the bifurcation mode is very useful for the natural responses of the system. 3) Among the perturbation techniques, HBM is a good estimate for the response when the geometry of motion is known. 4) It is known that there exist periodic solutions of coupled mode response for somewhat large damping and forcing amplitude, as well as weak damping and forcing. 5) The route-to-chaos related with lateral instability in thin beams is composed of period-doubling and quasiperiodic process and finally follows discontinuous period-doubling process. 6) The chaotic vibrations are verified by using Poincare maps, FFT's, time responses, trajectories in the configuration space, and the very powerful technique Lyapunov characteristics exponents.exponents.

• 대한수학회지
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• 제60권2호
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• 소음진동
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• 제8권3호
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• pp.408-419
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• 1998

Dynamic characteristics are investigated when a nonlinear system showing periodic and chaotic responses under harmonic excitation is exposed to random perturbation. Approach for both qulitative and quantitative analysis of the noise effect in a nonlinear system under harmonic excitation is presented. For the qualitative analysis, Lyapunov exponents are calculated and Poincar map is illustrated. For the quatitative analysis. Fokker-Planck equatin is solved numerical by means of a Path-integral solution procedure. Eigenvalue problem obtained from the numerical caculation is solved and the relation of eigenvalue, eigenvector and chaotic motion is investigated.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -3
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• pp.1992-1995
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• 2002

This paper presents a novel 4-D chaotic spiking oscillator. The oscillator can generate hyperchaos characterized by two positive Lyapunov exponents. Us-ing a simple test circuit, typical phenomena can be verified in the laboratory.

• Advances in nano research
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• 제15권1호
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• pp.25-34
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• 2023

This paper investigates the dynamics and stability of steady states in a continuous and discrete-time single-mode laser system. By using an explicit criteria we explored the Neimark-Sacker bifurcation of the single mode continuous and discrete-time laser model at its positive equilibrium points. Moreover, we discussed the parametric conditions for the existence of period-doubling bifurcations at their positive steady states for the discrete time system. Both types of bifurcations are verified by the Lyapunov exponents, while the maximum Lyapunov ensures chaotic and complex behaviour. Furthermore, in a three-dimensional discrete-time laser model, we used a hybrid control method to control period-doubling and Neimark-Sacker bifurcation. To validate our theoretical discussion, we provide some numerical simulations.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2007년도 추계 학술대회논문집
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• pp.49-55
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• 2007

The quality of chaotic mixing in three-dimensional micro channel flow has been numerically studied using Fractional-step method (FSM) and particle tracking techniques such as $Poincar{\acute{e}}$ section and Lyapunov exponents. The flow was driven by pressure distribution and the chaotic mixing was generated by applying alternating current to electrodes embedded on the bottom wall at a first half period and on the top wall at a second half period. The equations governing the velocity and concentration distributions were solved using FSM based on Finite Volume approach. Results showed that the mixing quality depended significantly on the modulation period. The modulation period for the best mixing performance was determined based on the mixing index for various initial conditions of concentration distribution. The optimal values of modulation period obtained by the particle tracking techniques were compared with those from the solution of concentration distribution equation using FSM and CFX software and the comparison showed their good match.