• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.195-215
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• 2005

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1893-1912
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• 2017

In this paper, we aim to construct a nonstandard finite difference (NSFD) scheme to solve numerically a mathematical model for cholera epidemic dynamics. We first show that if the basic reproduction number is less than unity, the disease-free equilibrium (DFE) is locally asymptotically stable. Moreover, we mainly establish the global stability analysis of the DFE and endemic equilibrium by using suitable Lyapunov functionals regardless of the time step size. Finally, numerical simulations with different time step sizes and initial conditions are carried out and comparisons are made with other well-known methods to illustrate the main theoretical results.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.379-403
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• 2018

In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.14-19
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• 1993

In this paper, we proposed an indirect learning and direct adaptive control schemes using neural networks, i.e., composite adaptive neural control, for a class of continuous nonlinear systems. With the indirect learning method, the neural network learns the nonlinear basis of the system inverse dynamics by a modified backpropagation learning rule. The basis spans the local vector space of inverse dynamics with the direct adaptation method when the indirect learning result is within a prescribed error tolerance, as such this method is closely related to the adaptive control methods. Also hash addressing technique, similar to the CMAC functional architecture, is introduced for partitioning network hidden nodes according to the system states, so global neuro control properties can be organized by the local ones. For uniform stability, the sliding mode control is introduced when the neural network has not sufficiently learned the system dynamics. With proper assumptions on the controlled system, global stability and tracking error convergence proof can be given. The performance of the proposed control scheme is demonstrated with the simulation results of a nonlinear system.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.6
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• pp.1542-1550
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• 1994

For a class of singularly perturbed uncertain system, an output feedback control law is designed. The controller structure is designed based on the uncertain reduced-order system, and the controller parameters are determined by information on the reduced-order and full-order systems. It has been shown that the reduces-order system with the designed controller possesses a stability property(specifically, a global uniform attractivity). Furthermore, the stability property of this control scheme is robust with respect to singular perturbation ; i.e., the full-order system, subject to the same controller, possesses the global uniform attractivity, provided the singular perturbation parameter $\mu<\mu^{*}$, where a threshold value $\mu^{*}$ can be computed from the information available on the full-order system.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.247-262
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• 2006

The main objective of this paper is to study the boundedness character, the periodic character and the global stability of the positive solutions of the following difference equation $x_{n+1}=\frac{{\alpha}x_n+{\beta}x_{n-1}+{\gamma}x_{n-2}+{\delta}x_{n-3}}{Ax_n+Bx_{n-1}+Cx_{n-2}+Dx{n-3}}$, n=0, 1, 1, ... where the coefficients A, B, C, D, ${\alpha},\;{\beta},\;{\gamma},\;{\delta}$ and the initial conditions x-3, x-2, x-1, x0 are arbitrary positive real numbers.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.217-230
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• 2017

In this paper we deal with the difference equation $$y_{n+1}=\frac{ay_{n-1}}{by_ny_{n-1}+cy_{n-1}y_{n-2}+d}$$, $$n{\in}\mathbb{N}_0$$, where the coefficients a, b, c, d are positive real numbers and the initial conditions $y_{-2}$, $y_{-1}$, $y_0$ are nonnegative real numbers. Here, we investigate global asymptotic stability, periodicity, boundedness and oscillation of positive solutions of the above equation.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.267-276
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• 2017

The purpose of this paper is to investigate the local asymptotic stability of equilibria, the periodic nature of solutions, the existence of unbounded solutions and the global behavior of solutions of the fractional difference equation $$x_{n+1}=\frac{^{{\alpha}x}n-1(k+1)}{{\beta}+{\gamma}x^p_{n-k}x^q_{n-(k+2)}}$$, $$n=0,1,{\dots}$$ where the parameters ${\alpha}$, ${\beta}$, ${\gamma}$, p, q are non-negative numbers and the initial values $x_{-(k+2)}$,$x_{-(k+1)}$, ${\dots}$, $x_{-1}$, $x_0{\in}\mathb{R}^+$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.7 s.178
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• pp.1689-1696
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• 2000

This paper proposes a new adaptive control scheme for flexible-link robots. A model-based nonlinear control scheme is designed based on a V-shape Lyapunov function, and then the nonlinear control i s extended to a model-based adaptive control to cope with parametric uncertainties in the dynamic model. The proposed control guarantees the global exponential or global asymptotic stability of the overall control system with all internal signals bounded. The effectiveness of the proposed control is shown by computer simulation.