• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.39-53
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• 2023

In this paper, we consider a delayed ratio-dependent predator-prey reaction-diffusion system with homogenous Neumann boundary conditions. We study the existence of nonnegative solutions and the stability of the nonnegative equilibria to the system. In particular, we provide a sufficient condition for the positive equilibrium to be globally asymptotically stable.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.385-398
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• 2013

In this paper, a turbidostat model with ratio-dependent growth rate and impulsive state feedback control is considered. We obtain sufficient conditions of the globally asymptotically stable of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.555-574
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• 2011

It is well known that the mathematical models provide very important information for the research of human immunodeciency virus type. However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T-cells and the viral particles. In this paper, a differential equation model of HIV infection of $CD4^+$ T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number $R_0$ < 1, the HIV infection is cleared from the T-cell population and the disease dies out; if $R_0$ > 1, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if $R_0$ > 1. Numerical simulations are presented to illustrate the results.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.2
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• pp.168-173
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• 2009

This paper investigates the estimation problem of vehicle velocity and propeller angular velocity on the underwater vehicle. Inspired by but different from a high-gain observer, the cascade observer features a cascade structure and adaptive observer gains. In doing so the cascade observer attempts to overcome some of the typical problems that may pose to a high-gain observer. As in the case of a high-gain observer, the cascade observer structure is simple and universal in the sense that it is independent of the system dynamics and parameters. A cascade observer is used for the estimation of velocity from measured position. In the 1st step of the observer, the output is estimated, and the 1st order derivative of measured output is estimated via the 2nd step of the observer. Also, nth order derivative of the output is estimated in the (n+1)th step of the observer. It is shown that the proposed observer guarantees globally asymptotical stability. By simulation results, the proposed observer scheme for the estimations of vehicle velocity and propeller angular velocity shows better performance than the scheme based on the existing observer.