• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.1
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• pp.57-64
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• 2002

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytical solutions of the system. The frequency-response curves sallow that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear Phenomena.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.228-230
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• 1997

Recently, as power systems become large and complicated, chaos theory has been introduced to analyze their nonlinear characteristics. In this paper, voltage collapse phenomenon is more accurately analyzed using bifurcation theory of chaos. Chaotic behaviors has been observed in computer simulation for a simple power system over a range of loading conditions. Besides existence of voltage collapse point in critical value, operation of power system in Hopf window can be the cause of voltage collapse.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.781-802
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• 2011

Of concern in the paper is a Holling-Tanner predator-prey model with modified version of the Leslie-Gower functional response. Dynamical behaviours such as stability, permanence and Hopf bifurcation have been carried out deterministically. Using the normal form theory and center manifold theorem, the explicit formulae determining the stability and direction of Hopf bifurcation have been derived. The deterministic model is extended to a stochastic one by perturbing the growth equation of prey and predator by white and colored noises and finally the mean square stability of the stochastic model systems is investigated analytically. An extensive quantitative analysis has been performed based on numerical computation so as to validate the applicability of the proposed mathematical model.

• Journal of Biomedical Engineering Research
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• v.18 no.2
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• pp.179-186
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• 1997

Steady and physiological flows of a Newtonian fluid and blood in the abdominal gorta/iliac artery bifurcation are numerically simulated to understand the etiology and pathogenesis of atherosclerosis. Distributions of velocity, pressure, and wall shear stress in the bifurcated arterial vessel model are calculated to investigate the differences of flow characteristics between steady and physiological flows and to compare flow characteristics of blood with that of a Newtonian fluid For the given Reynolds number the flow characteristics of physiological flows for a Newtonian fluid and blood in the bifurcated arterial vessel are quite different from thcse of steady flows. No flow separation or flow reversal in the bifurcated region appears downstream of a stenosis during the acceleration phase. However, during the deceleration phase the flow exhibits flow separation in the outer walls of daugtlter branches, which extends to the entire wall region.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.402-418
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• 2022

Noise is a fundamental factor to increased validity and regularity of spike propagation and neuronal firing in the nervous system. In this paper, we examine the stochastic version of the Izhikevich-FitzHugh neuron dynamical model. This approach is based on techniques presented by Luo and Guo, which provide a general framework for the bifurcation and stability analysis of two dimensional stochastic dynamical system as an Itô averaging diffusion system. By using largest lyapunov exponent, local and global stability of the stochastic system at the equilibrium point are investigated. We focus on the two kinds of stochastic bifurcations: the P-bifurcation and the D-bifurcations. By use of polar coordinate, Taylor expansion and stochastic averaging method, it is shown that there exists choices of diffusion and drift parameters such that these bifurcations occurs. Finally, numerical simulations in various viewpoints, including phase portrait, evolution in time and probability density, are presented to show the effects of the diffusion and drift coefficients that illustrate our theoretical results.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1113-1122
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• 2015

This paper is concerned with the pattern formation of a diffusive predator-prey model with two time delays. Based upon an analysis of Hopf bifurcation, we demonstrate that time delays can induce spatial patterns under some conditions. Moreover, by use of a series of numerical simulations, we show that the type of spatial patterns is the spiral wave. Finally, we demonstrate that the spiral wave is asymptotically stable.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.5.3-5
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• 2003

The boundary of a typical period-2 component in the degree-3 bifurcation set is formulated by a parametrization of its image which is the unit circle under the multiplier map, Some properties on the geometry of the boundary are investigated including the root point, the cusp, the component center and the length as well as the area bounded by the boundary curve. An algorithm drawing the boundary curve with Mathematica codes is proposed and its implementation exhibits a good agreement with the analysis presented here.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.69-78
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• 2004

This paper treats the conditions for the existence of rotating wave solutions of a system modelling the behavior of students in graduate programs at neighbouring universities near each other which is a modified form of the model proposed by Scheurle and Seydel. We assume that both types of individuals are continuously distributed throughout a bounded two-dimension spatial domain of two types (circle and annulus), across whose boundaries there is no migration, and which simultaneously undergo simple (Fickian) diffusion. We will show that at a critical value of a system-parameter bifurcation takes place: a rotating wave solution arises.

• 정보저장시스템학회:학술대회논문집
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• 2005.10a
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• pp.177-178
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• 2005

The load/unload behavior of the hard disk drive slider is studied in terms of the air bearing static characteristics. The numerical continuation methods are applied to calculate suspension force - equilibrium position curve. The critical preloads of the femto size slider are analyzed. The hi-stability conditions are depicted on the skew angle - preload diagram. The perturbation method is used to check the stability of the solution branches.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1614-1617
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• 2002

This paper studies basic phenomena of intermittently coupled capacitors circuits. As an analysis tool, we introduce Hybrid return map of real and binary variables, and analyze bifurcation phenomena for three parameters . Co-existence of synchronous phenomena is also shown. Using a simple test circuit, typical phenomena see verified in the laboratory.