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Displaying similar documents to “Asymptotic behavior of equilibrium point for a family of rational difference equations.”

On the rational recursive sequence x n + 1 = α 0 x n + α 1 x n - l + α 2 x n - k β 0 x n + β 1 x n - l + β 2 x n - k

E. M. E. Zayed, M. A. El-Moneam (2010)

Mathematica Bohemica

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The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation x n + 1 = α 0 x n + α 1 x n - l + α 2 x n - k β 0 x n + β 1 x n - l + β 2 x n - k , n = 0 , 1 , 2 , ⋯ where the coefficients α i , β i ∈ ( 0 , ∞ ) for i = 0 , 1 , 2 , and l , k are positive integers. The initial conditions x - k , ⋯ , x - l , ⋯ , x - 1 , x 0 are arbitrary positive real numbers such that l < k . Some numerical experiments are presented.