• Title/Summary/Keyword: Rational recursive sequence

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PERIODICITY AND ATTRACTIVITY FOR A RATIONAL RECURSIVE SEQUENCE

  • ZHANG LIJIE;ZHANG GUANG;LIU HUI
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.191-201
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    • 2005
  • In this paper, the existence of periodic positive solution and the attractivity are investigated for the rational recursive sequence $x_{n+1} = (A + ax_{n_k})/(b + x{n-l})$, where A, a and b are real numbers, k and l are nonnegative integer numbers.

ON THE RATIONAL RECURSIVE SEQUENCE $x_{n+1}=\frac{{\alpha}x_n+{\beta}x_{n-1}+{\gamma}x_{n-2}+{\delta}x_{n-3}}{Ax_n+Bx_{n-1}+Cx_{n-2}+Dx_{n-3}}$

  • Zayed E.M.E.;El-Moneam M.A.
    • 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.