• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1117-1127
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• 2011

In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.187-190
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• 1997

In the past few years, many researchers are interesting of control of mobile robot with nonholonomic constraints. And tracking problems is important as well as regulation in nonholonomic system control. Some researchers have investigated the stable tracking control law for mobile robot. But, few results showed the globally asymptotically stable control method simply. So, we address the design of globally asymptotically stable tracking control law for mobile robot with nonholonomic velocity constraints using simple method. The stabilizability of the controller is derived by Lyapunov direct method. And we analyze the system responses according to the variation of control parameters in line tracking problem. It is derived that the responses represent no overshoot property in line tracking. Examples are two-wheeled mobile robot and car-like mobile robot and the simulation results represent the effectiveness of our method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.1770-1773
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• 1997

In this paper, a linear discrete time system subject to the input saturatioin is shown to be exponentially stabilizable on any compact subset of the constrained asymptotically stabilizable set by a linear periodic variable structure controller. We also establish tat any neutrally stable system subject to the input saturation can be globally asymptotically stabilizable via linear feedback.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.31-56
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• 2007

In this paper, we consider a delay differential equation model of two competing species with harvesting of the mature and immature members of each species. The time delay in the model represents the time from birth to maturity of that species, which appears in the adults recruitment terms. We study the dynamics of our model analytically and we present results on positivity and boundedness of the solution, conditions for the existence and globally asymptotically stable of equilibria, a threshold of harvesting, and the optimal harvesting of the mature populations of each species.

• 대한수학회지
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• 제54권3호
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• pp.987-997
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• 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.

• 대한수학회지
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• 제58권1호
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• pp.45-67
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• 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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.1414-1417
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• 2003

In this paper, sliding mode controller for discrete-time nonlinear systems with uncertainties and disturbances are proposed. The concept of time-delay control (TDC) which consists of estimating the uncertain dynamics of the system through past observations of the system response is used. The proposed controller guarantees that the closed-loop system states are globally uniformly ultimately bounded (GUUB). It is also shown that the closed-loop system states are globally uniformly asymptotically stable (GUAS) if uncertainties are constant.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.797-804
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• 2010

The aim of this paper is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $x_{n+1}\;=\;\frac{A+Bx_{n-1}}{C+Dx_n^2}$, n = 0, 1, 2, ... where A, B are nonnegative real numbers and C, D > 0.

• 대한수학회지
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• 제49권4호
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• pp.779-794
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• 2012

In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, $CD4^+$ T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number $R_0$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.83.3-83
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• 2002

$\textbullet$ In this paper, a robust decentralized excitation control scheme is proposed $\textbullet$ We prove that the proposed control system is practically stable $\textbullet$ The origin is globally uniformly asymptotically stable in the absence of the disturbance $\textbullet$ If assumption is not satisfied, the proposed control system is still guarantees L2 stability $\textbullet$ Simulations for a three-machine power system demonstrates the effectiveness of the proposed scheme