• 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.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.695-713
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• 2013

We formulate and study a predator-prey model with non-monotonic functional response type and weak Allee effects on the prey, which extends the system studied by Ruan and Xiao in [Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J. Appl. Math. 61 (2001), no. 4, 1445-1472] but containing an extra term describing weak Allee effects on the prey. We obtain the global dynamics of the model by combining the global qualitative and bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the supercritical and the subcritical Hopf bifurcations, and the homoclinic bifurcation, as the values of parameters vary. In the generic case, the model has the bifurcation of cusp type of codimension 2 (i.e., Bogdanov-Takens bifurcation).

• The Transactions of the Korean Institute of Power Electronics
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• v.5 no.4
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• pp.394-402
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• 2000

This paper proposes a bifurcation theory method applied for voltage stability analysis and shows the improvement of voltage stability by attaching the FACTS devices in the power system. A power system is generally expressed by a set of equations of highly nonlinear dynamical system which includes system parameters(real or reactive power). Sometimes variation of parameters in the system may result in complication behaviors which give rise to system instability. The addition of FACTS increases the range of voltage stability in the power system. The effect of FACTS which improves voltage stability are illustrated in the case studies by delaying of Unstable Hopf Bifurcation and Saddle Node Bifurcation.

• Geomechanics and Engineering
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• v.9 no.5
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• pp.669-685
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• 2015

A three-dimensional elastoplastic constitutive model, also known as a UH model (Yao et al. 2009), was developed to describe the stress-strain relationship for normally consolidated and over-consolidated soils. In this paper, an acoustic tensor and discriminator of bifurcation for the UH model are derived for the strain localization of saturated clays under undrained and fully and partially drained conditions. Analytical analysis is performed to illustrate the points of bifurcation for the UH model with different three-dimensional stress paths. Numerical analyses of cubic specimens for the bifurcation of saturated clays under undrained and fully and partially drained conditions are conducted using ABAQUS with the UH model. Analytical and numerical analyses show the similar bifurcation behaviour of overconsolidated clays in three-dimensional stress states and various drainage conditions. The results of analytical and numerical analyses show that (1) the occurrence of bifurcation is dependent on the stress path and drainage condition; and (2) bifurcation can appear in either a strain-hardening or strain-softening regime.

• 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 Institute of Interior Design Journal
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• v.14 no.1
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• pp.20-27
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• 2005

This study is focused on the concept and spatial organization of bifurcation. After discussing the concept of bifurcation used in Borges' literature and Deleuze's Fold philosophy, case examples in contemporary architecture are analysed to comparatively investigate the relationship between the concept and space. In Deleuze's philosophy, bifurcation as well as pleats, inflection are used to form the world of fold that goes to infinity while, in Borges' literature, the structure of bifurcation is the key method to create the labyrinth of time. There are various projects in contemporary architecture based on the Deleuzian concept of bifurcation. Rem Koolhaas's Two Libraries for Jussieu University and UN Studio's Arnhem Central are selected and researched for further comparison study. In Jussieu project, the bifurcating spatial organization is 'intentionally' used to construct the indeterminant space whereas in Arnhem Central, bifurcation can be found in both the ever-bifurcating design process as well as the final spatial organization'unintentionally'generated from the process. This study is concluded with the comparative analysis between the representation and actualization of a concept that are crucially different.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.335-347
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• 2020

In this paper, we take into account a parasite-host system with reaction-diffusion. Firstly, we derive conditions for Hopf, Turing, and wave bifurcations of the system in the spatial domain by means of linear stability and bifurcation analysis. Secondly, we display numerical simulations in order to investigate Turing pattern formation. In fact, the numerical simulation discloses that typical Turing patterns, such as spotted, spot-stripelike mixtures and stripelike patterns, can be formed. In this study, we show that typical Turing patterns, which are well known in predator-prey systems ([7, 18, 25]), can be observed in a parasite-host system as well.

• 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.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04a
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• pp.353-358
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• 1998

The strain localization is a discontinuous phenomenon that addresses the formation of jumps of the field variables across a singularity surface. It has become widely accepted that the localization may occur as the result of discontinuous bifurcation which corresponds to the loss of ellipticity of the governing differential equations for elasto-plastic continua. In this paper, condition for strain localization in concrete based on bifurcation theory is studied and localization tensor analysis algorithm is employed to determine the directions of localization of deformations in concrete. By applying a plasticity model of concrete into the algorithm, localization analysis is performed concrete under uniaxial tension, pure shear and uniaxial compression.