Displaying similar documents to “On the recursive sequence x n + 1 = - 1 / x n + A / x n - 1 .”

On the rational recursive sequence x n + 1 = A + ∑ i = 0 k α i x n - i / ∑ i = 0 k β i x n - i

E. M. E. Zayed, M. A. El-Moneam (2008)

Mathematica Bohemica

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The main objective of this paper is to study the boundedness character, the periodic character, the convergence and the global stability of positive solutions of the difference equation x n + 1 = A + ∑ i = 0 k α i x n - i / ∑ i = 0 k β i x n - i , n = 0 , 1 , 2 , ⋯ where the coefficients A , α i , β i and the initial conditions x - k , x - k + 1 , ⋯ , x - 1 , x 0 are positive real numbers, while k is a positive integer number.

Some boundedness results for systems of two rational difference equations

Gabriel Lugo, Frank Palladino (2010)

Open Mathematics

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We study k th order systems of two rational difference equations x n = α + ∑ i = 1 k β i x n - 1 + ∑ i = 1 k γ i y n - 1 A + ∑ j = 1 k B j x n - j + ∑ j = 1 k C j y n - j , y n = p + ∑ i = 1 k δ i x n - i + ∑ i = 1 k ε i y n - i q + ∑ j = 1 k D j x n - j + ∑ j = 1 k E j y n - j n ∈ ℕ . In particular, we assume non-negative parameters and non-negative initial conditions, such that the denominators are nonzero. We develop several approaches which allow us to extend well known boundedness results on the k th order rational difference equation to the setting of systems in certain cases.