On a system of difference equations with period two coefficients (Q426973)
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scientific article; zbMATH DE number 6045829
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a system of difference equations with period two coefficients |
scientific article; zbMATH DE number 6045829 |
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On a system of difference equations with period two coefficients (English)
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13 June 2012
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system of rational difference equations
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period two coefficient
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explicit solution
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Considered is the following system of difference equations NEWLINE\[NEWLINE x_{n+1}=\frac{a_nx_{n-1}}{b_ny_nx_{n-1}+c_n}, \qquad y_{n+1}=\frac{\alpha_n y_{n-1}}{\beta_n x_ny_{n-1}+\gamma_n}, \qquad n\in \mathbb{N}_0, NEWLINE\]NEWLINE where the sequences \(a_n\), \(b_n\), \(c_n\), \(\alpha_n\), \(\beta_n\), \(\gamma_n\) are two-periodic and the initial values \(x_{-1}\), \(x_0\), \(y_{-1}\), \(y_0\) are real numbers. For the all possible cases, the author derives explicit formulae for all well-defined solutions. These results extend those in his paper [Appl. Math. Comput. 218, No. 14, 7649--7654 (2012; Zbl 1243.39011)].
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