• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1255-1262
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• 2012

A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.227-253
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• 2024

This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space BCL_-∞(H). We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.561-568
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• 2011

We investigate the stability property and existence of almost periodic solutions of discrete Volterra equations with unbounded delay.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1847-1854
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• 2013

The main concern of this paper is to study the dynamics of an n-dimensional ratio-dependent predator-prey system with diffusion. We study the dissipativeness, persistence of the system and it is shown that the unique positive constant steady state is globally asymptotically stable under some assumptions.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.575-587
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• 2006

In this paper, we provide 3 detailed and explicit procedure of obtaining some regions of attraction for the positive steady state (assumed to exist) of a well known Lotka-Volterra type predator-prey system. Also we obtain the sufficient conditions to ensure that the positive equilibrium point of a well known Lotka-Volterra type predator-prey system with a single discrete delay is globally asymptotically stable.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1901-1904
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• 2003

MPC or model predictive control is representative of control methods which are able to handle physical constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global aymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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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.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.15-26
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• 2002

In this paper, we suggest and analyze a class of resolvent dynamical systems associated with mixed variational inequalities. We study the globally asymptotic stability of the solution of the resolvent dynamical systems for the pseudomonotone operators. We also discuss some special cases, which can be obtained from our main results.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.439-445
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• 2007

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.2
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• pp.131-136
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• 2012

If one can find a control Lyapunov function (CLF) for a given nonlinear system, the control input stabilizing the system can be easily obtained. To find a CLF, the time derivative of an energy function should be negative definite. This procedure frequently requires a control input which is a rational function or includes an inverse function. The control input is not defined on the specific state-space where the denominator of the rational function is equal to 0 or the inverse function does not exist. In this region with singularities, the trajectory of the control system cannot be generated, which is one of the most important reasons why it is hard to make the origin of a nonlinear system be globally asymptotically stable. In this paper, we propose a smooth control law ensuring the globally asymptotic stability by means of cancelling the singularity in the control input.