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Displaying similar documents to “On the system of rational difference equations x n + 1 = f ( x n , y n - k ) , y n + 1 = f ( y n , x n - k ) .”

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.