• Title, Summary, Keyword: global stability

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STABILITY OF A CLASS OF DISCRETE-TIME PATHOGEN INFECTION MODELS WITH LATENTLY INFECTED CELLS

  • ELAIW, A.M.;ALSHAIKH, M.A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.22 no.4
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    • pp.253-287
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    • 2018
  • This paper studies the global stability of a class of discrete-time pathogen infection models with latently infected cells. The rate of pathogens infect the susceptible cells is taken as bilinear, saturation and general. The continuous-time models are discretized by using nonstandard finite difference scheme. The basic and global properties of the models are established. The global stability analysis of the equilibria is performed using Lyapunov method. The theoretical results are illustrated by numerical simulations.

GLOBAL EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS OF HIGH-ORDER HOPFIELD NEURAL NETWORKS WITH DISTRIBUTED DELAYS OF NEUTRAL TYPE

  • Zhao, Lili;Li, Yongkun
    • Journal of applied mathematics & informatics
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    • v.31 no.3_4
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    • pp.577-594
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    • 2013
  • In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

NEW CONDITIONS ON EXISTENCE AND GLOBAL ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS FOR BAM NEURAL NETWORKS WITH TIME-VARYING DELAYS

  • Zhang, Zhengqiu;Zhou, Zheng
    • Journal of the Korean Mathematical Society
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    • v.48 no.2
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    • pp.223-240
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    • 2011
  • In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

GLOBAL STABILITY OF A NONLINEAR DIFFERENCE EQUATION

  • Wang, Yanqin
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.879-889
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    • 2011
  • In this paper, we investigate the local asymptotic stability, the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation $x_{n+1}=\frac{a+bx_nx_{n-k}}{A+Bx_n+Cx_{n-k}}$, n = 0, 1,${\ldots}$, where the parameters a, b, A, B, C and the initial conditions $x_{-k}$, ${\ldots}$, $x_{-1}$, $x_0$ are positive real numbers.

GENERALIZED DISCRETE HALANAY INEQUALITIES AND THE ASYMPTOTIC BEHAVIOR OF NONLINEAR DISCRETE SYSTEMS

  • Xu, Liguang
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1555-1565
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    • 2013
  • In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].

EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF A PERIODIC SOLUTION TO DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS

  • Zhang, Zhengqiu;Wang, Liping
    • Journal of the Korean Mathematical Society
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    • v.48 no.4
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    • pp.727-747
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    • 2011
  • By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

GLOBAL STABILITY OF VIRUS DYNAMICS MODEL WITH IMMUNE RESPONSE, CELLULAR INFECTION AND HOLLING TYPE-II

  • ELAIW, A.M.;GHALEB, SH.A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.23 no.1
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    • pp.39-63
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    • 2019
  • In this paper, we study the effect of Cytotoxic T Lymphocyte (CTL) and antibody immune responses on the virus dynamics with both virus-to-cell and cell-to-cell transmissions. The infection rate is given by Holling type-II. We first show that the model is biologically acceptable by showing that the solutions of the model are nonnegative and bounded. We find the equilibria of the model and investigate their global stability analysis. We derive five threshold parameters which fully determine the existence and stability of the five equilibria of the model. The global stability of all equilibria of the model is proven using Lyapunov method and applying LaSalle's invariance principle. To support our theoretical results we have performed some numerical simulations for the model. The results show the CTL and antibody immune response can control the disease progression.

GLOBAL STABILITY OF A TUBERCULOSIS MODEL WITH n LATENT CLASSES

  • Moualeu, Dany Pascal;Bowong, Samuel;Emvudu, Yves
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1097-1115
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    • 2011
  • We consider the global stability of a general tuberculosis model with two differential infectivity, n classes of latent individuals and mass action incidence. This system exhibits the traditional threshold behavior. There is always a globally asymptotically stable equilibrium state. Depending on the value of the basic reproduction ratio $\mathcal{R}_0$, this state can be either endemic ($\mathcal{R}_0$ > 1), or infection-free ($\mathcal{R}_0{\leq}1$). The global stability of this model is derived through the use of Lyapunov stability theory and LaSalle's invariant set theorem. Both the analytical results and numerical simulations suggest that patients should be strongly encouraged to complete their treatment and sputum examination.

Global Asymptotic Stability of a Class of Nonlinear Time-Delay Systems (일종의 비선형 시간 지연 시스템에 대한 광역 점근적 안정성)

  • Choi, Joon-Young
    • Journal of Institute of Control, Robotics and Systems
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    • v.13 no.3
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    • pp.187-191
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    • 2007
  • We analyze the stability property of a class of nonlinear time-delay systems. We show that the state variable is bounded both below and above, and the lower and upper bounds of the state are obtained in terms of a system parameter by using the comparison lemma. We establish a time-delay independent sufficient condition for the global asymptotic stability by employing a Lyapunov-Krasovskii functional obtained from a change of the state variable. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.