• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권3호
• /
• pp.329-342
• /
• 2008

There have been many experimental and observational evidences which indicate the predator response to prey density needs not always monotone increasing as in the classical predator-prey models in population dynamics. Holling type functional response depicts situations in which sufficiently large number of the prey species increases their ability to defend or disguise themselves from the predator. In this paper we investigated the stability and instability property for a Holling type predator-prey system of a generalized form. Hopf type bifurcation properties of the non-diffusive system and the diffusion effects on instability and bifurcation values are studied.

• 대한기계학회논문집B
• /
• 제25권3호
• /
• pp.433-441
• /
• 2001

Natural convection of a fluid with intermediate Prand시 number of Pr=0.2 in a horizontal annulus is considered, and the bifurcation phenomena and chaotic flows are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. The steady downward flow with two counter-rotating eddies bifurcates to a simple periodic flow with a fundamental frequency. And afterwards, second Hopf bifurcation occurs, and a quasi-periodic flow with two incommensurable frequencies appears. However, a new time-periodic flow is established after experiencing quasi-periodic states. As Rayleigh number is increased further, the chaotic flow regime is reached after a sequence of successive Hopf bifurcation to quasi-periodic and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario of the onset of chaos is observed.

• 대한수학회보
• /
• 제54권2호
• /
• pp.655-666
• /
• 2017

In this paper, we study the pattern formation to a general Degn-Harrison reaction model. We show Turing instability happens by analyzing the stability of the unique positive equilibrium with respect to the PDE model and the corresponding ODE model, which indicate the existence of the non-constant steady state solutions. We also show the existence periodic solutions of the PDE model and the ODE model by using Hopf bifurcation theory. Numerical simulations are presented to verify and illustrate the theoretical results.

• Journal of applied mathematics & informatics
• /
• 제28권5_6호
• /
• pp.1379-1393
• /
• 2010

In this paper, a stage-structured predator prey model (stage structure on prey) with two discrete time delays has been discussed. The two discrete time delays occur due to maturation delay and gestation delay. Linear stability analysis for both non-delay as well as with delays reveals that certain thresholds have to be maintained for coexistence. Numerical simulation shows that the system exhibits Hopf bifurcation, resulting in a stable limit cycle.

• 한국소음진동공학회논문집
• /
• 제14권7호
• /
• pp.561-568
• /
• 2004

The nonlinear dynamic characteristic of a straight tube conveying fluid with constraints and an attached mass on the tube is examined in this study An experimental apparatus with an elastomer tube conveying water which has an attached mass and constraints is made and comparisons are made between the theoretical results from the non-linear equation of motion of piping system and the experimental results. The comparisons show that the tube is destabilized as the magnitude of the attached mass increases, and stabilized as the position of the attached mass closes to the fixed end. In case of a small end-mass, the system shows complicated and different types of solutions. For a constant end-mass. the system undergoes a series of bifurcations after the first Hopf bifurcation, as the flow velocity increases. which causes chaotic motions of the tube eventually.

• 대한기계학회논문집B
• /
• 제34권9호
• /
• pp.859-866
• /
• 2010

대향류 확산화염에서 확산-전도 불안정성에 의한 맥동불안정성의 비선형 거동을 수치 해석적으로 연구하였다. Lewis 수를 1보다 충분히 크게 두고 일차원 준정상상태의 화염의 해로부터 Damkohler 수를 섭동시켜 시간에 따른 화염의 전개를 계산하였다. 맥동 불안정성에 의한 비선형 화염전개는 세 가지 다른 형태, 즉 교란이 점점 감소되는 경우, 교란이 증폭되어 안정된 주기적 진동이 일어나는 경우, 그리고 교란이 계속 증폭되어 화염이 소염되는 경우 등으로 나타났다. 스트레치를 받지 않는 화염의 결과와 달리 대향류 유동장의 화염에서는 안정된 한계순환 맥동 불안정이 존재하였다. 세 가지 다른 형태의 화염 전개를 보이는 임계 Damkohler 수를 계산하여 동적 소염이 일어나는 영역을 표시하였고, 이는 층류소화염의 국소소염 계산에 이용될 수 있다. 불안정성이 나타나는 갈래질의 구조는 초임계 및 임계이하 Hopf 갈래질로 나타났다. 특정한 Damkohler 수의 영역에서 안정된 한계 순환 갈래질이 나타났으며, 화염온도가 증가함에 따라 영역이 축소되어 안정된 한계순환이 일어나는 영역은 사라지고 불안정한 한계순환 갈래질이 나타났다. 안정된 한계순환 영역이 확장되는 영역이 존재하며, 이는 단순한 한계순환 불안정성이 주기배증에 의한 Rossler 갈래질이 나타나면서 한계 영역이 확장되었다.

• 대한기계학회논문집B
• /
• 제20권9호
• /
• pp.2965-2972
• /
• 1996

Transitional flow in an obstructed channel is investigated using numerical simulation. Two-dimensional thin obstacles are mounted symmetrically in the vertical direction and periodically in the streamwise direction. Flow separation occurs at the tip of the sharp obstacles. Depending on the Reynolds number, the flow undergoes Hopf bifurcation as the primary instability leading to a two-dimensional unsteady periodic solution. At higher Reynolds numbers, the unsteady solution exhibits a symmetry-breaking bifurcation which results in an unsteady asymmetric solution. The results are compared with experiments currently available, and show a good agreement.

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

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제4권1호
• /
• pp.61-69
• /
• 1997

In this paper, we study the dynamics of a two-parameter unfolding system $\chi$' = y, y' = $\beta$y＋$\alpha$f($\chi\alpha\pm\chiy$＋yg($\chi$), where f($\chi$,$\alpha$) is a second order polynomial in $\chi$ and g($\chi$) is strictly nonlinear in $\chi$. We show that the higher order term yg($\chi$) in the system does not change qulitative structure of the Hopf bifurcations near the fixed points for small $\alpha$ and $\beta$ if the nontrivial fixed point approaches to the origin as $\alpha$ approaches zero.

• 대한수학회보
• /
• 제33권4호
• /
• pp.631-638
• /
• 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 $\Omega = (0,1) \times (0, \infty)$.