• 한국유체기계학회 논문집
• /
• 제10권1호
• /
• pp.7-13
• /
• 2007

This study proposes a modified bifurcation model with a computational fluid analysis according to variation of a bifurcation geometry. FLUENT is used for a calculation of the head losses in case of a generation and a pumping. The pressure, velocity field and turbulent intensity are simulated in a bifurcation. With consideration about these flow properties, we propose the modified model to improve a flow efficiency and reduce a sound. The proposed model is able to cut down a head loss by 45% when a generation and 36% when a pumping.

• 대한수학회지
• /
• 제54권1호
• /
• pp.1-16
• /
• 2017

In this paper we study a four dimensional tourism-based social-ecological dynamical system. In fact we analyse tourism profitability, compatibility and sustainability by using bifurcation theory in terms of structural properties of attractors of system. For this purpose first we transformed it into a three dimensional system such that the reduced system is the extended and modified model of the previous three dimensional models suggested for tourism with the same dimension. Then we investigate transcritical, pitchfork and saddle-node bifurcation points of system. And numerically by finding some branches of stable equilibria for system show the profitability of tourism industry. Then by determining the Hopf bifurcation points of system we find a family of stable attractors for that by numerical techniques. Finally we conclude the existence of these stable limit cycles implies profitability and compatibility and then the sustainability of tourism.

• Kyungpook Mathematical Journal
• /
• 제50권2호
• /
• pp.255-266
• /
• 2010

We consider a delayed predator-prey system with Holling II functional response. Firstly, the paper considers the stability and local Hopf bifurcation for a delayed prey-predator model using the basic theorem on zeros of general transcendental function, which was established by Cook etc.. Secondly, special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations supporting the theoretical analysis are given.

• 유체기계공업학회:학술대회논문집
• /
• 유체기계공업학회 2005년도 연구개발 발표회 논문집
• /
• pp.789-795
• /
• 2005

This study proposes a modified bifurcation model with a computational fluid analysis according to variation of a bifurcation geometry. FLUENT is used for a calculation of the head losses in case of a generation and a pumping. The pressure, velocity field and turbulent intensity are simulated in a bifurcation. With consideration about these flow properties, we propose the modified model to improve a flow efficiency and reduce a sound. The proposed model is able to cut down a head loss by 45% when a generation and 36% when a pumping.

• 한국산학기술학회논문지
• /
• 제7권6호
• /
• pp.1421-1424
• /
• 2006

본 논문은 맨델브로트 집합을 9차 복소 다항식에 확장시켜 새로운 프랙탈 도형을 나타내는 9차 분기집합을 정의하고, 2주기 성분의 경계방정식을 매개함수로 표현한다. 또한, 2주기 성분을 작도하는 알고리즘을 고안하고, 매스매티카를 활용하여 2주기 성분의 기하학적 구조에 관한 결과를 제시하고자 한다.

• Advances in nano research
• /
• 제15권1호
• /
• pp.25-34
• /
• 2023

This paper investigates the dynamics and stability of steady states in a continuous and discrete-time single-mode laser system. By using an explicit criteria we explored the Neimark-Sacker bifurcation of the single mode continuous and discrete-time laser model at its positive equilibrium points. Moreover, we discussed the parametric conditions for the existence of period-doubling bifurcations at their positive steady states for the discrete time system. Both types of bifurcations are verified by the Lyapunov exponents, while the maximum Lyapunov ensures chaotic and complex behaviour. Furthermore, in a three-dimensional discrete-time laser model, we used a hybrid control method to control period-doubling and Neimark-Sacker bifurcation. To validate our theoretical discussion, we provide some numerical simulations.

• 대한기계학회논문집B
• /
• 제28권6호
• /
• pp.697-704
• /
• 2004

Bifurcation behavior of ignition and extinction of catalytic reaction is theoretically investigated in a stagnation-point flow. Considering that reaction takes place only on the catalytic surface, where conductive heat losses are allowed to occur, activation energy asymptotics with a overall one-step Arrhenius-type catalytic reaction is employed. For the cases with and without the limiting reactant consumption, the analysis provides explicit expressions, which indicate the possibility of multiple steady-state solution branches. The difference between the solutions with and without reactant consumption is in the existence of an upper solution branch, and the neglect of reactant consumption is inappropriate for determining extinction conditions. For larger values of reactant consumption, the solution response is all monotone, suggesting that multiple solutions are not possible. It is shown that bifurcation Damkohler numbers increase (decrease) with increasing of conductive heat loss (gain) on the catalytic surface, which means that smaller (larger) values of the strain rate allow the surface reaction to tolerate larger heat losses (gains). Lewis number of the limiting reactant can also significantly affect bifurcation behavior in a similar way to the effect of heat loss.

• 한국전산유체공학회지
• /
• 제16권4호
• /
• pp.64-71
• /
• 2011

Cerebral aneurysm mostly occurs at a bifurcation of the circle of Willis. When the cerebral aneurysm is ruptured, a disease like subarachnoid hemorrhage and stroke is caused and this can be even deadly for patients. Generally it is known that causes of the intracranial aneurysm are a congenital deformity of the artery and pressure or shear stress from the blood flow. A blood flow pattern and the geometry of the blood vessel are important factors for the aneurysm formation. Research for several hemodynamic indices has been performed and these indices can be used for the prediction of aneurysm initiation and rupture. Therefore, the numerical analysis was performed for hemodynamic characteristics of the blood flow through the cerebral artery applying the various bifurcation angle and flow rate ratio. We analyze the flow characteristics using indices from the results of the numerical simulation. In addition, to investigate the flow pattern in the aneurysm according to the bifurcation angle and the flow rate ratio, we performed the numerical simulation on the supposition that the aneurysm occurs.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2011년 춘계학술대회논문집
• /
• pp.161-168
• /
• 2011

Cerebral aneurysm mostly occurs at a bifurcation of the circle of Willis. When the cerebral aneurysm is ruptured a disease like subarachnoid hemorrhage and stroke is caused and this can be even deadly for patients. Generally it is known that causes of the intracranial aneurysm are a congenital deformity of the artery and pressure or shear stress from the blood flow. A blood flow pattern and the geometry of the blood vessel are important factors for the aneurysm formation. Research for several hemodynamic indices has been performed and these indices can be used for the prediction of aneurysm initiation and rupture. Therefore, the numerical analysis was performed for hemodynamic characteristics of the blood flow through the cerebral artery applying the various bifurcation angle and flow rate ratio. We analyze the flow characteristics using indices from the results of the numerical simulation. In addition, to investigate the flow pattern in the aneurysm according to the bifurcation angle and the flow rate ratio, we performed the numerical simulation on the supposition that the aneurysm occurs.

• 한국항공운항학회지
• /
• 제21권4호
• /
• pp.47-52
• /
• 2013

In this paper, limit cycle flutter induced by Hopf bifurcation is studied with nonlinear system analysis approach and observed for the critical slowing down phenomenon. Considering an attractor of the dynamics of a system, when a small perturbation is applied to the system, the dynamics converge toward the attractor at some rate. The critical slowing down means that this recovery rate approaches zero as a parameter of the system varies and the size of the basin of attraction shrinks to nil. Consequently, in the pre-bifurcation regime, the recovery rates decrease as the system approaches the bifurcation. This phenomenon is one of the features used to forecast bifurcation before they actually occur. Therefore, studying the critical slowing down for limit cycle flutter behavior would have potential applicability for forecasting those types of flutter. Herein, modeling and nonlinear system analysis of the 2D airfoil with torsional nonlinearity have been discussed, followed by observation of the critical slowing down phenomenon.