• Title, Summary, Keyword: asymptotic equilibrium

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ON ASYMPTOTIC PROPERTY IN VARIATION FOR NONLINEAR DIFFERENTIAL SYSTEMS

  • Choi, Sung Kyu;Im, Dong Man;Koo, Namjip
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.545-556
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    • 2009
  • We show that two notions of asymptotic equilibrium and asymptotic equilibrium in variation for nonlinear differential systems are equivalent via $t_{\infty}$-similarity of associated variational systems. Moreover, we study the asymptotic equivalence between nonlinear system and its variational system.

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ASYMPTOTIC BEHAVIORS FOR LINEAR DIFFERENCE SYSTEMS

  • IM DONG MAN;GOO YOON HOE
    • The Pure and Applied Mathematics
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    • v.12 no.2
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    • pp.93-103
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    • 2005
  • We study some stability properties and asymptotic behavior for linear difference systems by using the results in [W. F. Trench: Linear asymptotic equilibrium and uniform, exponential, and strict stability of linear difference systems. Comput. Math. Appl. 36 (1998), no. 10-12, pp. 261-267].

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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.

ASYMPTOTIC STABILITY OF COMPETING SPECIES

  • Kim, June Gi
    • Korean Journal of Mathematics
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    • v.4 no.1
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    • pp.39-43
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    • 1996
  • Large-time asymptotic behavior of the solutions of interacting population reaction-diffusion systems are considered. Polynomial stability was proved.

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THE ASYMPTOTIC STABILITY BEHAVIOR IN A LOTKA-VOLTERRA TYPE PREDATOR-PREY SYSTEM

  • Ko, Youn-Hee
    • 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.