Some boundedness results for systems of two rational difference equations

Gabriel Lugo; Frank Palladino

Open Mathematics, Tome 8 (2010), p. 1058-1090 / Harvested from The Polish Digital Mathematics Library

Résumé

We study k th order systems of two rational difference equations $x_{n} = \frac{α + \sum_{i = 1}^{k} β_{i} x_{n - 1} + \sum_{i = 1}^{k} γ_{i} y_{n - 1}}{A + \sum_{j = 1}^{k} B_{j} x_{n - j} + \sum_{j = 1}^{k} C_{j} y_{n - j}}, y_{n} = \frac{p + \sum_{i = 1}^{k} δ_{i} x_{n - i} + \sum_{i = 1}^{k} ε_{i} y_{n - i}}{q + \sum_{j = 1}^{k} D_{j} x_{n - j} + \sum_{j = 1}^{k} E_{j} y_{n - j}} n \in ℕ$ . 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.

Publié le : 2010-01-01

Zbl 1218.39011

EUDML-ID : urn:eudml:doc:269538

@article{bwmeta1.element.doi-10_2478_s11533-010-0063-y,
     author = {Gabriel Lugo and Frank Palladino},
     title = {Some boundedness results for systems of two rational difference equations},
     journal = {Open Mathematics},
     volume = {8},
     year = {2010},
     pages = {1058-1090},
     zbl = {1218.39011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0063-y}
}

Gabriel Lugo; Frank Palladino. Some boundedness results for systems of two rational difference equations. Open Mathematics, Tome 8 (2010) pp. 1058-1090. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0063-y/

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