• Proceedings of the KIEE Conference
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• 1999.07c
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• pp.1308-1310
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• 1999

The addition of SVC increases the range of dynamic stability in the power system. The inclusion of SVC is explained in detail and a numerical example is presented. The entire construction of the system A matrix is analyzed, and then the effect of SVC on Hopf bifurcations and the PV curves are illustrated in the cabs study.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.327-344
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• 2005

The first part of the paper deals with a brief introduction of the plant-herbivore model system along with deterministic analysis of local stability and Hopf-bifurcations. The second part consists of stability analysis of the limit cycle arising from Hopf-bifurcation and uniqueness of limit cycle. The third part deals with the study of global stability of the model system under consideration.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.1-22
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• 2011

In this paper, a Lotka-Volterra model with time delays is considered. A set of sufficient conditions for the existence of Hopf bifurcation are obtained via analyzing the associated characteristic transcendental equation. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form method and center manifold theory. Finally, the main results are illustrated by some numerical simulations.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.504-514
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• 2003

We investigate global bifurcation in the subharmonic motion of a circular plate with one-to-one internal resonance. A system of autonomous equations are obtained from the partial differential equations governing the system by using Galerkin's procedure and the method of multiple scales. A perturbation method developed by Kovacic and Wiggins is used to find Silnikov type homoclinic orbits. The conditions under which the orbits occur are obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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• pp.249-256
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• 2012

In this work, we analyze the spatial patterns of a predator-prey system with cross diffusion. First we get the critical lines of Hopf and Turing bifurcations in a spatial domain by using mathematical theory. More specifically, the exact Turing region is given in a two parameter space. Our results reveal that cross diffusion can induce stationary patterns which may be useful in understanding the dynamics of the real ecosystems better.

• 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 KIEE Conference
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• 1996.11a
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• pp.88-90
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• 1996

In this paper center manifold theory is reviewed and its application to the control of bifurcations is explored. When applying the theory to a sample power system, we study the stabilization of bifurcation points using controls depending only on the rotor angular velocity of a generator. Under such a control it is shown that the system is not locally stabilizable when control is applied through mechanical power, and the system is locally stabilizable when the control is applied to the capacitor compensator.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.321-338
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• 2011

In this paper, a class of delayed epidemic model with diffusion is investigated. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation are also carried out to support our analytical findings. Finally, biological explanations and main conclusions are given.

• Journal of Korean Neurosurgical Society
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• v.49 no.2
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• pp.102-106
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• 2011

Objective : Although there are several explanations for a duplicated middle cerebral artery (DMCA), its embryological origin is still an open question. We reviewed these anomalous vessels to postulate a theory of their different origins, sizes, and courses. Methods : A retrospective review of 1,250 cerebral angiographies, 1,452 computed tomography (CT)-angiographies, and 2,527 magnetic resonance (MR)-angiographies was performed to identify patients with DMCA. Results : Twenty-five patients had 25 DMCAs. Conventional angiography detected nine patients with DMCA (9/1250, 0.72%), MR-angiography detected seven patients with DMCA 0.28%), and CT-angiography detected nine patients with DMCA (9/1452, 0.62%). The DMCAs originated near the internal carotid artery terminal in eight patients (type A), and between the origin of the anterior choroidal artery and the terminal internal carotid artery in 17 patients (type B). The diameters of the eight type A DMCAs were the same or slightly smaller than those of the other branch of the DMCA. All type A DMCAs showed a course parallel to that of the other branch of the DMCA. The diameters of the 17 type B DMCAs were the same, slightly smaller, or very much smaller than that of the other branch of the DMCA. Nine type B DMCAs showed parallel courses, and the other eight curved toward the temporal lobe. Conclusion : The two branches of the type A DMCAs can be regarded as early bifurcations of the MCA. The branches of the type B DMCAs had parallel courses or a course that curved toward the temporal lobe. The type B DMCA can be regarded as direct bifurcations of the MCA trunk or the early ramification of the temporal branch of the MCA.