### On the system of rational difference equations ${x}_{n+1}=f({y}_{n-q},{x}_{n-s})$, ${y}_{n+1}=g({x}_{n-t},{y}_{n-p})$.

Sun, Taixiang, Xi, Hongjian (2006)

Advances in Difference Equations [electronic only]

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Sun, Taixiang, Xi, Hongjian (2006)

Advances in Difference Equations [electronic only]

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Gabriel Lugo, Frank Palladino (2010)

Open Mathematics

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We study k th order systems of two rational difference equations $${x}_{n}=\frac{\alpha +{\sum}_{i=1}^{k}{\beta}_{i}{x}_{n-1}+{\sum}_{i=1}^{k}{\gamma}_{i}{y}_{n-1}}{A+{\sum}_{j=1}^{k}{B}_{j}{x}_{n-j}+{\sum}_{j=1}^{k}{C}_{j}{y}_{n-j}},{y}_{n}=\frac{p+{\sum}_{i=1}^{k}{\delta}_{i}{x}_{n-i}+{\sum}_{i=1}^{k}{\epsilon}_{i}{y}_{n-i}}{q+{\sum}_{j=1}^{k}{D}_{j}{x}_{n-j}+{\sum}_{j=1}^{k}{E}_{j}{y}_{n-j}}n\in \mathbb{N}$$ . 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.

Sun, Taixiang, Xi, Hongjian, Hong, Liang (2006)

Advances in Difference Equations [electronic only]

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