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Solution and Attractivity for a Rational Recursive Sequence

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  • E. M. Elsayed

Abstract

This paper is concerned with the behavior of solution of the nonlinear difference equation ð ‘¥ ð ‘› + 1 = ð ‘Ž ð ‘¥ ð ‘› − 1 + ð ‘ ð ‘¥ ð ‘› ð ‘¥ ð ‘› − 1 / ( ð ‘ ð ‘¥ ð ‘› + ð ‘‘ ð ‘¥ ð ‘› − 2 ) , ð ‘› = 0 , 1 , … , where the initial conditions ð ‘¥ − 2 , ð ‘¥ − 1 , ð ‘¥ 0 are arbitrary positive real numbers and ð ‘Ž , ð ‘ , ð ‘ , ð ‘‘ are positive constants. Also, we give specific form of the solution of four special cases of this equation.

Suggested Citation

  • E. M. Elsayed, 2011. "Solution and Attractivity for a Rational Recursive Sequence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-17, June.
    • Handle: RePEc:hin:jnddns:982309
    DOI: 10.1155/2011/982309
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    Cited by:

    1. Khalil S. Al-Basyouni & Elsayed M. Elsayed, 2023. "On Some Solvable Systems of Some Rational Difference Equations of Third Order," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    2. Hashem Althagafi & Ahmed Ghezal, 2024. "Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations," Mathematics, MDPI, vol. 12(8), pages 1-20, April.
    3. Abdul Khaliq & E.M. Elsayed, 2016. "Qualitative Properties of Difference Equation of Order Six," Mathematics, MDPI, vol. 4(2), pages 1-14, April.

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