• Title/Summary/Keyword: global attractivity

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OSCILLATION AND ATTRACTIVITY OF DISCRETE NONLINEAR DELAY POPULATION MODEL

  • Saker, S.H.
    • Journal of applied mathematics & informatics
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    • v.25 no.1_2
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    • pp.363-374
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    • 2007
  • In this paper, we consider the discrete nonlinear delay model which describe the control of a single population of cells. We establish a sufficient condition for oscillation of all positive solutions about the positive equilibrium point and give a sufficient condition for the global attractivity of the equilibrium point. The oscillation condition guarantees the prevalence of the population about the positive steady sate and the global attractivity condition guarantees the nonexistence of dynamical diseases on the population.

GLOBAL ATTRACTIVITY OF THE RECURSIVE SEQUENCE $x_{n+1}$ = $\frac{\alpha-{\beta}x_{n-1}}{\gamma+g(x_n)}$

  • Ahmed, A. M.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.275-282
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    • 2008
  • Our aim in this paper is to investigate the global attractivity of the recursive sequence $x_{n+1}$ = $\frac{\alpha-{\beta}x_{n-1}}{\gamma+g(x_n)}$ under specified conditions. We show that the positive (or zero for $\alpha$ = 0) equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients and the function g(x).

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Global Attractivity and Oscillations in a Nonlinear Impulsive Parabolic Equation with Delay

  • Wang, Xiao;Li, Zhixiang
    • Kyungpook Mathematical Journal
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    • v.48 no.4
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    • pp.593-611
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    • 2008
  • Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models $$\array{\{{{\frac {{\partial}u(t,x)}{{\partial}t}=\Delta}u(t,x)-{\delta}u(t,x)+f(u(t-\tau,x)),\;t{\neq}t_k,\\u(t^+_k,x)-u(t_k,x)=g_k(u(t_k,x)),\;k{\in}I_\infty,}\;\;\;\;\;\;\;\;(*)$$ are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of (*) with Neumann boundary condition are established. These results no only are true but also improve and complement existing results for (*) without diffusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.

ON THE RECURSIVE SEQUENCE $x_{n+l} =\alpha+\frac{x_{n-1}^{p}}{x_{n}^{p}}$

  • STEVIC STEVO
    • Journal of applied mathematics & informatics
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    • v.18 no.1_2
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    • pp.229-234
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    • 2005
  • The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form $x_{n+l} =\alpha+\frac{x_{n-1}^{p}}{x_{n}^{p}},\;\; n = 0, 1, ...$ is investigated, where all the coefficients are nonnegative real numbers.

OSCILLATION AND GLOBAL ATTRACTIVITY IN A PERIODIC DELAY HEMATOPOIESIS MODE

  • Saker, S.H.
    • Journal of applied mathematics & informatics
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    • v.13 no.1_2
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    • pp.287-300
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    • 2003
  • In this paper we shall consider the nonlinear delay differential equation (equation omitted) where m is a positive integer, ${\beta}$(t) and $\delta$(t) are positive periodic functions of period $\omega$. In the nondelay case we shall show that (*) has a unique positive periodic solution (equation omitted), and show that (equation omitted) is a global attractor all other positive solutions. In the delay case we shall present sufficient conditions for the oscillation of all positive solutions of (*) about (equation omitted), and establish sufficient conditions for the global attractivity of (equation omitted). Our results extend and improve the well known results in the autonomous case.

ON THE RECURSIVE SEQUENCE X_{n+1} = $\alpha$ - (X_n/X_n-1)

  • YAN XING XUE;LI WAN TONG;ZHAO ZHU
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.269-282
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    • 2005
  • We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n+1}\;=\;{\alpha}-{\frac{x_{n-1}}{x_{n}},\;n=0,1,\;{\cdots}$$, where ${\alpha}\;\in\; R$ is a real number, and the initial conditions $x_{-1},\;x_0$ are arbitrary real numbers.

GLOBAL ATTRACTIVITY OF THE RECURSIVE SEQUENCE $x_{n+1}\;=\;\frac{{\alpha}\;-\;{\beta}x_{n-\kappa}}{{\gamma}+x_n}$

  • El-Owaidy, H.M.;Ahmed, A.M.;Elsady, Z.
    • Journal of applied mathematics & informatics
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    • v.16 no.1_2
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    • pp.243-249
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    • 2004
  • Our aim in this paper is to investigate the global attractivity of the recursive sequence $x_{n+1}\;=\;\frac{{\alpha}\;-\;{\beta}x_{n-\kappa}}{{\gamma}+x_n}$, where ${\alpha},\;{\beta},\;{\gamma}\;>\;0\;and\;{kappa}\;=\;1,\;2,\;{\ldots}$ We show that the positive equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients.

PERMANENCE FOR THREE SPECIES PREDATOR-PREY SYSTEM WITH DELAYED STAGE-STRUCTURE AND IMPULSIVE PERTURBATIONS ON PREDATORS

  • Zhang, Shuwen;Tan, Dejun
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1097-1107
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    • 2009
  • In this paper, three species stage-structured predator-prey model with time delayed and periodic constant impulsive perturbations of predator at fixed times is proposed and investigated. We show that the conditions for the global attractivity of prey(pest)-extinction periodic solution and permanence of the system. Our model exhibits a new modelling method which is applied to investigate impulsive delay differential equations. Our results give some reasonable suggestions for pest management.

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Robust Deterministic Control of Singularly Perturbed Uncertain Systems (특이섭동 불확실시스템의 견실확정제어)

  • 강철구
    • 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.