• 대한기계학회논문집B
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• 제20권9호
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• pp.2973-2980
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• 1996

Secondary instability in an obstructed channel is investigated using direct numerical simulation. Flow geometry under consideration is a plane channel with two-dimensional thin obstacles mounted symmetrically in the vertical direction and periodically in the streamwise direction. Flow separation occurs at the tip of the sharp obstacles. As a basic flow, we consider an unsteady periodic solution which results from Hopf bifurcation. Depending on the Reynolds number, the basic flow becomes unstable to three-dimensional disturbances, which results in a chaotic flow. Numerical results obtained are consistent with experimental findings currently available.

• 한국전산유체공학회지
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• 제16권3호
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• pp.52-58
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• 2011

This study investigates the bifurcation sequence to chaos in a horizontal annulus with a constant heat flux wall. After the first Hopf bifurcation from a steady to a simple time-periodic flow with a fundamental frequency, quasi-periodic flows with two or three incommensurable frequencies appear. A reverse transition from a quasi-periodic flow to a simple periodic flow is observed with increase of Rayleigh number. And finally, chaotic convection is established after appearance of three incommensurable frequencies at a high Rayleigh number. Simple periodic flows exist between quasi periodic flows. The transition route to chaos of the present simulations follows the Ruelle-Takens route.

• 대한수학회지
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• 제49권4호
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• pp.715-731
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• 2012

This paper considers the stability of positive steady-state solutions bifurcating from the trivial solution in a delayed Lotka-Volterra two-species predator-prey diffusion system with a discrete delay and subject to the homogeneous Dirichlet boundary conditions on a general bounded open spatial domain with smooth boundary. The existence, uniqueness and asymptotic expressions of small positive steady-sate solutions bifurcating from the trivial solution are given by using the implicit function theorem. By regarding the time delay as the bifurcation parameter and analyzing in detail the eigenvalue problems of system at the positive steady-state solutions, the asymptotic stability of bifurcating steady-state solutions is studied. It is demonstrated that the bifurcating steady-state solutions are asymptotically stable when the delay is less than a certain critical value and is unstable when the delay is greater than this critical value and the system under consideration can undergo a Hopf bifurcation at the bifurcating steady-state solutions when the delay crosses through a sequence of critical values.

• 대한수학회논문집
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• 제34권2호
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• pp.685-699
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• 2019

This research is focused on a continuous epidemic model of transmission of Plasmodium vivax malaria with a time delay. The model is represented as a system of ordinary differential equations with delay. There are two equilibria, which are the disease-free state and the endemic equilibrium, depending on the basic reproduction number, $R_0$, which is calculated and decreases with the time delay. Moreover, the disease-free equilibrium is locally asymptotically stable if $R_0<1$. If $R_0>1$, a unique endemic steady state exists and is locally stable. Furthermore, Hopf bifurcation is applied to determine the conditions for periodic solutions.

• 대한수학회지
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• 제42권5호
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• pp.1071-1086
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• 2005

In this paper, we introduce a discrete time to the model to describe the time between infection of a CD4$^{+}$ T-cells, and the emission of viral particles on a cellular level. We study the effect of the time delay on the stability of the endemically infected equilibrium, criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. We also obtain the condition for existence of an orbitally asymptotically stable periodic solution.

• 대한수학회보
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• 제33권4호
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• pp.631-638
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• 1996

The parabolic free boundary problem with Puschino dynamics is given by (see in [3]) $$ (1) { \upsilon_t = D\upsilon_{xx} - (c_1 + b)\upsilon + c_1 H(x - s(t)) for (x,t) \in \Omega^- \cup \Omega^+, { \upsilon_x(0,t) = 0 = \upsilon_x(1,t) for t > 0, { \upsilon(x,0) = \upsilon_0(x) for 0 \leq x \leq 1, { \tau\frac{dt}{ds} = C)\upsilon(s(t),t)) for t > 0, { s(0) = s_0, 0 < s_0 < 1, $$ where $\upsilon(x,t)$ and $\upsilon_x(x,t)$ are assumed continuous in $\Omega = (0,1) \times (0, \infty)$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권4호
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• pp.249-256
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• 2012

In this work, we analyze the spatial patterns of a predator-prey system with cross diffusion. First we get the critical lines of Hopf and Turing bifurcations in a spatial domain by using mathematical theory. More specifically, the exact Turing region is given in a two parameter space. Our results reveal that cross diffusion can induce stationary patterns which may be useful in understanding the dynamics of the real ecosystems better.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.385-395
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• 2007

The dynamics of a prey-predator system, where predator population has two stages, juvenile and adult with harvesting are modelled by a system of delay differential equation. Our analysis shows that, both the delay and harvesting effort may play a significant role on the stability of the system. Numerical simulations are given to illustrate the results.

• 한국소음진동공학회논문집
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• 제24권1호
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• pp.14-20
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• 2014

Recent developments for high altitude, long endurance conventional UAVs(HALE UAVs) have revealed new issues regarding aircraft structure design and analysis. First of all, due to intensive mission requirements, the structures of HALE UAVs have lightweight and very flexible main wing with high aspect ratio, and slender fuselage. For this kind of structures, aeroelastic characteristics are different from conventional aircrafts. Hence, currently developed analysis methods are not suitable to fully understand strucutral dynamics of the very flexible aircraft, and to guarantee structural reliability. Therefore, various structural studies considering nonlinear behaviors which are generally ignored for the conventional aircraft strucutral analyis have been attracting researchers interests. Nonlinear flutter of the very flexible wing is one of the subject to be studied in combination with strong coupling between aeroelastic characteristics and flight dynamics. Herein, as preliminary study, modeling and nonlinear system analysis of the 2D airfoild with torsional nonlinearity have been discussed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 추계학술대회 논문집
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• pp.226-231
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• 2013

Recent developments for high altitude, long endurance conventional UAVs (HALE UAVs) have revealed new issues regarding aircraft structure design and analysis. First of all, due to intensive mission requirements, the structures of HALE UAVs have lightweight and very flexible main wing with high aspect ratio, and slender fuselage. For this kind of structures, aeroelastic characteristics are different from conventional aircrafts. Hence, currently developed analysis methods are not suitable to fully understand strucutral dynamics of the very flexible aircraft, and to guarantee structural reliability. Therefore, various structural studies considering nonlinear behaviors which are generally ignored for the conventional aircraft strucutral analyis have been attracting researchers interests. Nonlinear flutter of the very flexible wing is one of the subject to be studied in combination with strong coupling between aeroelastic characteristics and flight dynamics. Herein, as preliminary study, modeling and nonlinear system analysis of the 2D airfoild with torsional nonlinearity have been discussed.