• Journal of applied mathematics & informatics
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• 제10권1_2호
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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.

• 대한수학회지
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• 제50권4호
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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).

• 전력전자학회논문지
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• 제5권4호
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• pp.394-402
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• 2000

본 논문온 전압안정도에 Brfurcation 이론을 적용하여 해석하고, FACTS기가인 SVC와 UPFC를 전력계통에 연계하였을 때 전압안정도가 향상되는 효과를 보여주고 있다. 전압안정도는 일반적으로 시스템 파라미터(유효전력 또는 무효전력}를 포행하는 고도의 비선형 동적시스템의 식들에 의해 표현된다. 때때로 전력계통에서의 파라미터 변이는 시스템 불안정을 일으키는 복잡한 동작을 일으킬 수도 있다. 전력계통에서의 FACTS의 연계는 이러한 전압안정도의 범위를 증가시킨다. FACTS를 이용하여 불안정한 HopF Bifurcation과 Saddle Node Bihlfcation을 지연시킴에 의해서 전압안정도기 향상됨을 사례연구를 통하여 입증하였다.

• Geomechanics and Engineering
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• 제9권5호
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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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.

• 한국실내디자인학회논문집
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• 제14권1호
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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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• 제60권2호
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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.

• 한국생물정보학회:학술대회논문집
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• 한국생물정보시스템생물학회 2004년도 The 3rd Annual Conference for The Korean Society for Bioinformatics Association of Asian Societies for Bioinformatics 2004 Symposium
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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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• 제13권4호
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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.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1998년도 봄 학술발표회 논문집(I)
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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.