• Journal of the Korean Mathematical Society
• /
• v.42 no.5
• /
• pp.1071-1086
• /
• 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.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.30 no.3B
• /
• pp.305-313
• /
• 2010

River restoration or rehabilitation should be conducted in a way to maximize the channel stability with natural river configuration close to the equilibrium condition considering divers aspects of fluvial hydraulics, erosion and sedimentation, fluvial geomorphology, and ecological environment and to minimize the maintenance work. Therefore, the channel stability evaluation for present condition based on the equilibrium channel concept should be preceded for the river restoration project. Methods for equilibrium channel theory have generally been developed following either analytical regime theory or empirical regime theory. The main purpose of this paper is to evaluate the stability of present channel condition for the section of abandoned channel restoration in Cheongmi Stream using the Stable channel Analytical Model (SAM) and equilibrium hydraulic geometry equations. The results of analytical and empirical regime theories should provide fundamental and essential information to design the stable channel geometry. As a calculation result of Copeland's method for the study reach, the equilibrium channel has a narrower channel width, deeper water depth, and more gentle slope than the present channel geometry. As results of equilibrium hydraulic geometry equations, predicted equilibrium widths are less than the channel width in the field. It is represented that the current bed slope must be gentle to reach the equilibrium condition according to the results of Julien and Wargadalam method.

• Journal of Korean Society on Water Environment
• /
• v.27 no.4
• /
• pp.438-444
• /
• 2011

Magnesium is one of the abundant natural resources in the earth crust and seawater, which is directly related to various organisms activities interconnecting with water-rock system. In aqueous system, magnesium is known to predominantly exist in the form of $Mg^{2+}$ ion which is verified in its $E_h-pH$ diagram. When it is at equilibrium in aqueous system, temperature takes an essential role to complete equilibrium states. This study represents the change of the stable region of magnesium ion according to temperature, and how the consequences would affect aquatic organisms. It was revealed that there is a noticeable tendency shrinking the stable region of magnesium ion in a diagram as temperature increases, and as a result, aquatic bio-species presumably have difficulties to absorb the nutrient. Also, it was considered that the water system would be acidified by decreasing alkalinity.

• Journal of Institute of Control, Robotics and Systems
• /
• v.18 no.5
• /
• pp.496-501
• /
• 2012

An equilibrium point of a WIP (Wheeled Inverted Pendulum) with changing its center of gravity is derived and validated by various numerical simulations. Generally, the WIP has two equilibrium points which are unstable and stable one. The unstable one is interested in this study. To keep the WIP over the unstable equilibrium point, the WIP is consistently being adjusted. A state feedback controller for the WIP needs a control reference for the equilibrium point. The control reference can be obtained by studying an equilibrium point of the WIP based on statics. By using Lagrange method, this study is deriving dynamic equations of the WIP both with and without changing its center of gravity. Various numerical simulations are carried out to show the validation of the equilibrium point.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.207-210
• /
• 1997

In this paper, a hierarchical fuzzy controller for stabilization of the inverted pendulum system is proposed. The facility of this hierarchical fuzzy controller which has a swing-up control mode and a stabilization one, moves a pendulum in an initial natural stable equilibrium point and a cart in arbitrary position to an unstable equilibrium point and a center of rail. Specially, the virtual equilibrium point (.PHI.$_{VEq}$ ) which describes functionally considers the interactive dynamics between a position of cart and a angle of inverted pendulum is introduced. And comparing with the convention optimal controller, the proposed hierarchical fuzzy inference made substantially the inverted pendulum system robust and stable.e.

• Journal of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.987-997
• /
• 2017

A deterministic model for the spread of pine wilt disease with asymptomatic carrier trees in the host pine population is designed and rigorously analyzed. We have taken four different classes for the trees, namely susceptible, exposed, asymptomatic carrier and infected, and two different classes for the vector population, namely susceptible and infected. A complete global analysis of the model is given, which reveals that the global dynamics of the disease is completely determined by the associated basic reproduction number, denoted by $\mathcal{R}_0$. If $\mathcal{R}_0$ is less than one, the disease-free equilibrium is globally asymptotically stable, and in such a case, the endemic equilibrium does not exist. If $\mathcal{R}_0$ is greater than one, the disease persists and the unique endemic equilibrium is globally asymptotically stable.

• Proceedings of the KIEE Conference
• /
• 1997.11a
• /
• pp.83-85
• /
• 1997

In this paper, a self-tunning fuzzy inference technique for stabilization of the inverted pendulum system is proposed. The facility of this self-tunning fuzzy controller which has swing-up control mode and a stabilization one, moves a pendulum in an initial natural stable equilibrium point and a cart in arbitrary position, to an unstable equilibrium point and a center of rail. Specially, the virtual equilibrium point(${\phi}_{VEq}$) which describes functionally considers the interactive dynamics between a position of cart and a angle of inverted pendulum is introduced. And comparing with the convention optimal controller, the proposed self-tunning fuzzy inference structure made substantially the inverted pendulum system robust and stable.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.10a
• /
• pp.304-309
• /
• 1998

In this paper, a fuzzy controller for stabilization of the inverted pendulum system is propose. The facility of this fuzzy controller which has a swing-up control mode and a stabilization one, moves a pendulum in an initial natural stable equilibrium point and a cart in arbitary position, to an unstable equilibrium point and a center of rail. Specially, the virtual equilibrium point ($\Phi$veq) which describes functionally considers the interactive dynamics between a position of cart and a angle of inverted pendulum is introduced. And comparing with the convention optimal controller, the proposed hierarchical fuzzy inference structur made substantially the inverted pendulum system robust and stable.

• Journal of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.45-67
• /
• 2021

In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic "SIR" epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if ��d > 1, then the endemic equilibrium is globally asymptotically stable. However, if ��d ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if ��s > 1, the disease is stochastically permanent with full probability. However, if ��s ≤ 1, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.529-546
• /
• 2011

A deterministic tuberculosis model for theoretically assessing the potential impact of the combined effects of case detection in the presence of treatment is formulated. The qualitative features of its equilibria are analyzed and it is found that the disease-free equilibrium may not be globally asymptotically stable when the reproduction number is less than unity. This disease threshold number is further used to assess the impact of active TB case finding alone and in conjunction with treatment. A critical threshold parameter ${\Theta}$ say for which case detection will have a positive impact is derived. Using the Centre Manifold theory, the model may exhibit the phenomenon of backward bifurcation (coexistence of a locally stable endemic equilibrium with a stable disease-free equilibrium) when the reproduction number is less than unity. It is shown that the possibility of backward bifurcation occurring decreases with increase case detection. Graphical representations suggest that increase in case finding accompanied by treatment of detected TB cases, result in a marked decrease of TB cases (both latent and active TB).