• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1191-1205
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• 2008

We consider a delayed predator prey model. The local stability and Hopf bifurcation results are stated taking the time delay as a control parameter. We apply multiple scale analysis to analyze the effects of additive white noises near the Hopf bifurcation point at the positive interior equilibrium state. The governing equations for the amplitude of oscillations on a slow time scale are derived. We identify the process of amplitude of oscillations and derive its transient properties. We show that oscillations, which would decay in the deterministic system whenever time delay lies below its critical value, persists for long time under the validity of multiple scale analysis.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1997년도 추계학술대회 논문집 학회본부
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• pp.228-230
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• 1997

Recently, as power systems become large and complicated, chaos theory has been introduced to analyze their nonlinear characteristics. In this paper, voltage collapse phenomenon is more accurately analyzed using bifurcation theory of chaos. Chaotic behaviors has been observed in computer simulation for a simple power system over a range of loading conditions. Besides existence of voltage collapse point in critical value, operation of power system in Hopf window can be the cause of voltage collapse.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 가을 학술발표회 논문집
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• pp.277-284
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• 2003

One of important problem, in large space structure, is to overcome the self-weight of roof structure. This problem can be solved with using tension members effectively. Thus the rapid progress of hybrid structure, that makes effective use of the means of settling, has a good effect on realizing the large space. These systems of hybrid structure have the advantages of light weight and its own internal redundancy, but are occurred unstable phenomenon such as bifurcation or snap-through buckling, when the load level is come to the critical point. Among the hybrid structure, cable dome is shown the strong nonlinearity of unstable phenomenon in accordance with the external force. Therefore, the purpose of this study is to analyze and verify comparatively the unstable phenomenon of the Geiger and Flower type cable dome structures under axismmetric load.

• 호남수학학술지
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• 제44권3호
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• pp.402-418
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• 2022

Noise is a fundamental factor to increased validity and regularity of spike propagation and neuronal firing in the nervous system. In this paper, we examine the stochastic version of the Izhikevich-FitzHugh neuron dynamical model. This approach is based on techniques presented by Luo and Guo, which provide a general framework for the bifurcation and stability analysis of two dimensional stochastic dynamical system as an Itô averaging diffusion system. By using largest lyapunov exponent, local and global stability of the stochastic system at the equilibrium point are investigated. We focus on the two kinds of stochastic bifurcations: the P-bifurcation and the D-bifurcations. By use of polar coordinate, Taylor expansion and stochastic averaging method, it is shown that there exists choices of diffusion and drift parameters such that these bifurcations occurs. Finally, numerical simulations in various viewpoints, including phase portrait, evolution in time and probability density, are presented to show the effects of the diffusion and drift coefficients that illustrate our theoretical results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권2호
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• pp.203-220
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• 2023

A new modification of the SIS epidemic model incorporating the adaptive host behavior is proposed. Unlike the common situation in most epidemic models, this system has two disease-free equilibrium points, and we were able to prove that as the basic reproduction number approaches the threshold of 1, these two points merge and a Bogdanov-Takens bifurcation of codimension three occurs. The occurrence of this bifurcation is a sign of the complexity of the dynamics of the system near the value 1 of basic reproduction number. Both local and global stability of disease-free and endemic equilibrium point are studied.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.119-132
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• 2022

Virotherapy is an effective method for the treatment of cancer. The oncolytic virus specifically infects the lyse cancer cell without harming normal cells. There is a time delay between the time of interaction of the virus with the tumor cells and the time when the tumor cells become infectious and produce new virus particles. Several types of viruses are used in virotherapy and the delay varies with the type of virus. This delay can play an important role in the success of virotherapy. Our present study is to explore the impact of this delay in cancer virotherapy through a mathematical model based on delay differential equations. The partial success of virotherapy is guarenteed when one gets a stable non-trivial equilibrium with a low level of tumor cells. There exits Hopf-bifurcation by considering the delay as bifurcation parameter. We have estimated the length of delay which preserves the stability of the non-trivial equilibrium point. So when the delay is less than a threshold value, we can predict partial success of virotherapy for suitable sets of parameters. Here numerical simulations are also performed to support the analytical findings.

• 대한기계학회논문집A
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• 제20권11호
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• pp.3441-3453
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• 1996

A finite element anlaysis is performed for large deformations of a felxible beam. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. The finite elements results are confirmed for several cases of deformations through comparison to a first order elasticity solution obtained by numerical integration, and the agreement between the two is found to be excellent. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformation in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement.

• 한국해양공학회지
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• 제11권4호
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• pp.7-22
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• 1997

A finite element analysis is performed for lateral buckling problems on the basis of a geometrically nonlinear formulation for a beam with small elastic strain but with possibly large rotations. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformations in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement. This is illustrated through several numerical examples and followed by appropriate discussion.

• 한국초전도ㆍ저온공학회논문지
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• 제2권2호
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• pp.15-19
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• 2000

The stability of variable cross-sectional area HTS current lead is considered. The cross-sectional area is varied to have a constant safety factor which is defined as the ratio of operating current and critical current of superconductor. As the constant area HTS lead, the variable cross-sectional area HTS lead also has three steady states above the bifurcation point and only one steady state below the bifurcation point. The temperature profiles and current sharing ratios for each steady state are calculated. The heat dissipation into cryogenic system for super-conducting, intermediate, and upper states are compared. For Bi-2333 sheathed with silver-gold alloy 2m length of current lead, and the maximum temperature of upper state seems to be burn-out free below 5m length.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1999년도 가을 학술발표회 논문집
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• pp.395-402
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• 1999

This paper discusses the theoretical researches subject to elastic buckling problems of the structures. The purpose is to ensure the characteristic of buckling be true by arc-length method and the finite element method. The difficulties in processes calculating the equilibrium curve after buckling is to get the equilibrium owe near singular point at which the determinant of stiffness matrix is zero. The purpose of the load-displacement curve is to determine the buckling load of the structure, and further to get the information about the characteristic after buckling. Here, this paper expresses the incremental solution at particular point by the linear combination of both homogeneous mode and particular mode, then uses the method which gets the unknown parameter including this function, through trial-and-error method including modified N-R convergence process. Finally, this paper describes the multiple bifurcation of truss dome as the numerical examples according to this algorithm.