• Korean Journal of Mathematics
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• v.22 no.3
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• pp.471-489
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• 2014

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.28-31
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• 1997

Buckling analysis of thin compressed beam has been carried out. Pre-buckling and post-buckling are simulated by finite element method incorporating with the incremental nonlinear theory and the Newton-Raphson solution technique. In order to find the bifurcation point, the determinent of the stiffness matrix is calculated at every iteration procedure. For post-buckling analysis, a small perturbed initial guess is given along the eigenvector direction at the bifurcation point. Nonlinear elastic buckling and elastic-plastic buckling of cantilever beam are analyzed. The buckling load and buckled shape of the two models are compared.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.637-647
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• 1999

In this paper, we consider a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition. We shall the stationary solutions ($v^{*}(x),s^{*}$) exist and the Hopf bifurcation occurs at a critical point when s $\in$ (1/3,1).

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2005.09a
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• pp.278-283
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• 2005

Cell cycle is regulated cooperatively by several genes. The dynamic regulatory mechanism of protein interaction network of cell cycle will be presented taking the budding yeast as a sample system. Based on the mathematical model developed by Chen et at. (MBC, 11,369), at first, the dynamic role of the feedback loops is investigated. Secondly, using a bifurcation diagram, dynamic analysis of the cell cycle regulation is illustrated. The bifurcation diagram is a kind of ‘dynamic road map’ with stable and unstable solutions. On the map, a stable solution denotes a ‘road’ attracting the state and an unstable solution ‘a repelling road’ The ‘START’ transition, the initiation of the cell cycle, occurs at the point where the dynamic road changes from a fixed point to an oscillatory solution. The 'FINISH' transition, the completion of a cell cycle, is returning back to the initial state. The bifurcation analysis for the mutants could be used uncovering the role of proteins in the cell cycle regulation network.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.307-314
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• 2009

The present paper briefly describes the space frame element and the fundamental strategies in computational elastic bifurcation theory of geometrically nonlinear, single load parameter conservative elastic spatial structures. A method for large deformation(rotation) analysis of space frame is based on an eulerian formulation, which takes into consideration the effects of large joint translations and rotations with finite deformation(rotation). The local member force-deformation relationships are based on the beam-column approach, and the change in member chord lengths caused by axial strain and flexural bowing are taken into account. and the derived geometric stiffness matrix is unsymmetric because of the fact that finite rotations are not commutative under addition. To detect the singular point such as bifurcation point, an iterative pin-pointing algorithm is proposed. And the path switching mode for bifurcation path is based on the non-negative eigen-value and it's corresponding eigen-vector. Some numerical examples for bifurcation analysis are carried out for a plane frame, plane circular arch and space dome structures are described.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.447-470
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• 2016

Limit cycle oscillations (LCO) as well as nonlinear aeroelastic analysis of a swept aircraft wing with cubic restoring moments in the pitch degree of freedom is investigated. The unsteady aerodynamic loading applied on the wing is modeled by using the strip theory. The harmonic balance method is used to calculate the LCO frequency and amplitude for the swept wing. Finally the super and subcritical Hopf bifurcation diagrams are plotted. It is concluded that the type of bifurcation and turning point location is sensitive to the system parameters such as wing geometry and sweep angle.

• Journal of Electrical Engineering and Technology
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• v.1 no.1
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• pp.80-84
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• 2006

The sustained oscillation of rotor speed is often experienced in PWM inverter induction motor (IM) drive systems. In this paper the oscillation is investigated from the point of view of Hopf bifurcation theory. The sufficient and necessary conditions for existence of limit cycle are introduced to determine the bifurcation set in the stator voltage versus stator frequency plane. According to the conditions it is clarified that the bifurcation set inherently exists in the instable operation of IM. Moreover, it is numerically shown that the V/f curve can be adjusted to stabilize the sustained oscillation of rotor speed.

• Journal of Korea Water Resources Association
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• v.52 no.1
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• pp.1-10
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• 2019

This study investigates the flow characteristics, such as velocity distributions, size and location of recirculation zone, longitudinal flow change rates, and bifurcation discharge ratio in the bifurcation channel by TELEMAC-2D, a 2D numerical model. The numerical model is validated by previous experimental results and the numerical results are in relatively good agreement with the experimental results, such as the water surface elevation and velocity distribution in the channels. As the inertial force and moment in the main channel decrease, the bifurcation discharge ratio increases, and the relative high velocity distribution becomes wider and the reverse velocity of the main stream decreases in the branch channel. As the bifurcation discharge ratio increases, the size of the recirculation zone in the branch channel decreases and it can be more clearly calculated by determining the point where the longitudinal froude number $Fr{\approx}0$ as well as drawing the distribution of the streamline distribution.

• 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.

• Computational Structural Engineering
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• v.9 no.3
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• pp.209-216
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• 1996

The primary objective of this paper is to grasp many characteristics of buckling behavior of latticed spherical domes under various conditions. The Arc-Length Method proposed by E.Riks is used for the computation and evaluation of geometrically nonlinear fundamental equilibrium paths and bifurcation points. And the direction of the path after the bifurcation point is decided by means of Hosono's concept. Three different nonlinear stiffness matrices of the Slope-Deflection Method are derived for the system with rigid nodes and results of the numerical analysis are examined in regard to geometrical parameters such as slenderness ratio, half-open angle, boundary conditions, and various loading types. But in case of analytical model 2 (rigid node), the post-buckling path could not be surveyed because of Newton-Raphson iteration process being diversed on the critical point since many eigenvalues become zero simultaneously.