• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.339-350
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• 2006

The bifurcation point where a satellite component buds from another component is characterized by the existence of the common tangent line between the two osculating components appearing in the degree-n bifurcation set. We investigate the existence, location and number of bifurcation points for satellite components budding from the main component in the degree-n bifurcation set as well as a parametric boundary equation of the main component of the degree-n bifurcation set. Cusp points are also located on the boundary of the main component. Typical degree-n bifurcation sets and their components are illustrated with some computational results.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.17-26
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• 2002

A stability analysis of a non-linear prey-predator system under the influence of one dimensional diffusion has been investigated to determine the nature of the bifurcation point of the system. The non-linear bifurcation analysis determining the steady state solution beyond the critical point enables us to determine characteristic features of the spatial inhomogeneous pattern arising out of the bifurcation of the state of the system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.853-861
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• 2007

To understand the concept of dynamic motion in two degree nonlinear coupled system, free vibration not including damping and excitation is investigated with the concept of nonlinear normal mode. Stability analysis of a coupled system is conducted, and the theoretical analysis performed for the bifurcation phenomenon in the system. Bifurcation point is estimated using harmonic balance method. When the bifurcation occurs, the saddle point is always found on Poincare's map. Nonlinear phenomenon result in amplitude modulation near the saddle point and the internal resonance in the system making continuous interchange of energy. If the bifurcation in the normal mode is local, the motion remains stable for a long time even when the total energy is increased in the system. On the other hand, if the bifurcation is global, the motion in the normal mode disappears into the chaos range as the range becomes gradually large.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.269-275
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• 1990

Nonaxisymmetric bifurcation behaviours of composite tubes two different materials subjected to uniform radial shrinkage at the external surface have been investigated and compared with those of single tube. The effect of material parameters normalized with respect to those of outer tube upon the bifurcation point and corresponding mode has been clarified. The parameters substantially affect the bifurcation mode with long-wavelength so that the composite tube with low hardening exponent or with high yield stress of inner tube destabilizes the overall deformation of the tube. However surface type bifurcation, short-wavelength mode, shown on the traction-free inner surface is hardly affected by the material parameters. The surface type bifurcation completely depends on the material characteristics of inner tube and the bifurcation point of composite tube almost coincides with the of single tube.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.113-124
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• 2006

In this paper we consider the numerical solution of the sunflower equation. We prove that if the sunflower equation has a Hopf bifurcation point at a = ao, then the numerical solution with the Euler-method of the equation has a Hopf bifurcation point at ah = ao + O(h).

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.95-102
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• 1994

A path-switching strategy by combining the use of generalized inverse and line search is proposed. A reliable predictor for the tangent vector to bifurcation path is first computed by using the generalized inverse approach. A line search in the direction of maximum gradient of total potential at the point of intersection between the above predictor and a constant loading plane introduced in the vicinity of the detected bifurcation point is then carried out for the purpose of obtaining an improved approximation for a point on bifurcation path. With this approximation obtained, an actual point on bifurcation path is then computed through iteration on the constant loading plane.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.2
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• pp.43-57
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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 and the length as well as the area bounded by the boundary curve. The centroid of the area for the period-2 component was numerically found with high accuracy and compared with its center. An algorithm drawing the boundary curve with Mathematica codes is proposed and its implementation exhibits a good agreement with the analysis presented here.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.2
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• pp.252-263
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• 1997

Steady-state two-dimensional natural convective heat transfer in horizontal cylindrical annuli was studied by solving the governing equations based on the primitive variables. Emphasis was put on the occurrence of the multiple solutions at a given set of parameter values, and on the determination of the bifurcation points at which those multiple solutions begin to branch out. The multicellular flow pattern from the results of melting process in an isothermally heated horizontal cylinder for high Rayleigh numbers, was used as initial guesses for the field variables. This was succeeded in new bifurcation point to tetracellular solutions for an identical set of parameter variables of previous works. The close examination of flow pattern transition around bifurcation point was also conducted. It was found that the mechanisms of flow transition are different depending on the critical Rayleigh number of bifurcation point.

• Structural Engineering and Mechanics
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• v.16 no.2
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• pp.141-152
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• 2003

Characteristics of solutions of softening plasticity are discussed in this article. The localized and non-localized solutions are obtained for a three-bar truss and their stability is evaluated with the aid of the second-order work. Beyond the bifurcation point, the single stable loading path splits into several post-bifurcation paths and the second-order work exhibits several competing minima. Among the multiple post-bifurcation equilibrium states, the localized solutions correspond to the minimum points of the second-order work, while the non-localized solutions correspond to the saddles and local maximum points. To determine the real post-bifurcation path, it is proposed that the structure should follow the path corresponding to the absolute minimum point of the second-order work. The proposal is further proved equivalent to Bazant's path criterion derived on a thermodynamics basis.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1149-1167
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• 2015

We get a theorem which shows the existence of at least four $2{\pi}$-periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory.