• 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1241-1252
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• 2015

In this paper, we study the dynamical bifurcation of the modified Swift-Hohenberg equation on a periodic interval as the system control parameter crosses through a critical number. This critical number depends on the period. We show that there happens the pitchfork bifurcation under the spatially even periodic condition. We also prove that in the general periodic condition the equation bifurcates to an attractor which is homeomorphic to a circle and consists of steady states solutions.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.309-312
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• 1997

The dynamic characteristics of a continuous MMA/MA free-radical solution copolymerization reactor were studied. A mathematical model was developed and kinetic parameters which had been estimated in the previous work were used. With this model, bifurcation diagrams were constructed with various parameters as the bifurcation parameter to predict the region of stable operating conditions and to enhance the controller performance. It was shown that the steady-state multiplicity existed over wide ranges of residence time and jacket inlet temperature. Periodic solution branches were found to emanated from Hopf bifurcation points. Under certain conditions isola was also observed, which would result in poor performance of feedback controllers.

• International Journal of Fluid Machinery and Systems
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• v.10 no.1
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• pp.1-8
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• 2017

Bifurcation refers to wye division of penstock to divide the flow symmetrically or unsymmetrically into two units of turbine for maintaining economical, technical and geological substrates. Particularly, water shows irrelevant behavior when there is a sudden change in flow direction, which results into the transition of the static and dynamic behavior of the flow. Hence, special care and design considerations are required both hydraulically and structurally. The transition induced losses and extra stresses are major features to be examined. The research on design and analysis of bifurcation is one of the oldest topics related to R&D of hydro-mechanical components for hydropower plants. As far as the earlier approaches are concerned, the hydraulic designs were performed based on graphical data sheet, head loss considerations and the mechanical analysis through simplified beam approach. In this paper, the multi prospect approach for design of Bifurcation, incorporating the modern day's tools and technology is identified. The hydraulic design of bifurcation is a major function of dynamic characteristics of the flow, which is performed with CFD analysis for minimum losses and better hydraulic performances. Additionally, for the mechanical design, a simplified conventional design method as pre-estimation and Finite Element Method for a relevant result projections were used.

• 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.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.637-645
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• 2016

In this paper, we study dynamical Bifurcation of the Burgers-Fisher equation. We show that the equation bifurcates an invariant set ${\mathcal{A}}_n({\beta})$ as the control parameter ${\beta}$ crosses over $n^2$ with $n{\in}{\mathbb{N}}$. It turns out that ${\mathcal{A}}_n({\beta})$ is homeomorphic to $S^1$, the unit circle.

• Structural Engineering and Mechanics
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• v.40 no.3
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• pp.335-346
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• 2011

This paper deals with the bifurcations of non-semi-simple eigenvalues at critical point of Hopf bifurcation to understand the dynamic behavior of the system. By using the Puiseux expansion, the expression of the bifurcation of non-semi-simple eigenvalues and the corresponding topological structure in the parameter space are obtained. The zero-order approximate solutions in the vicinity of the critical points at which the multiple Hopf bifurcation may occur are developed. A numerical example, the flutter problem of an airfoil in simplified model, is given to illustrate the application of the proposed method.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2004.11a
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• pp.50-56
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• 2004

Bifurcation analysis of cell cycle regulation in the budding yeast is performed basedon the mathematical model by Chen et al [Molecular biology of cell, 11:369-391, 2000]. On the bifurcation diagram, locations of both stable and unstable solutions of the nonlinear differential equations are presented by taking the mass of cell as a controlparameter. Based on the bifurcation diagram, dynamic mechanism underlying the 'start' transition, initiation of a new round of cell cycle, and the 'finish' transition, completion of cell cycle and returning back to the initial state, is discussed: the 'start' transition is a transition from a stable fixed solution for a small mass and to an oscillatory state for a large mass, and the 'finish' transition is a switching back to the stable fixed solution from the oscillatory state. To understand the role of the genes during the cell cycle regulation, bifurcation diagrams for the mutants are compared with that of the wild type.

• Advances in nano research
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• v.13 no.4
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• pp.379-391
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• 2022

One factor that can heighten the risk of the rapture intracranial aneurysm (IA) is bifurcations, which can cause the IA to evaluate. This study presents the effect of geometric of intracranial vascular on the bifurcation analysis of the aneurysm occurrence. The aneurysm mechanism is mathematically modeled based on the nano pipe structures under the thermal stresses, and the impact of the aneurysm geometric on the stability and bifurcation points is analyzed. Because of the dimension of these structures, the classical theories could not predict their behavior perfectly, so the nonclassical and nonlocal theories are required for the mechanical modeling of the aneurysm. The presented results show that the bifurcation point of the aneurysm mechanism is dependent on the environment temperature, and the temperature change plays an essential role in the stability of these structures.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.923-937
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• 2012

In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic cell ${\Omega}=[-L,L]$. It is shown that the equations bifurcates from the trivial solution to an attractor $\mathcal{A}_{\lambda}$ when th control parameter ${\lambda}$ crosses the critical value. In the odd periodic case $\mathcal{A}_{\lambda}$ is homeomorphic to $S^1$ and consists of eight singular points and thei connecting orbits. In the periodic case, $\mathcal{A}_{\lambda}$ is homeomorphic to $S^1$, an contains a torus and two circles which consist of singular points.