Some boundedness results for systems of two rational difference equations

Gabriel Lugo, and Frank Palladino. "Some boundedness results for systems of two rational difference equations." Open Mathematics 8.6 (2010): 1058-1090. <http://eudml.org/doc/269538>.

@article{GabrielLugo2010,
abstract = {We study k th order systems of two rational difference equations \[ x\_n = \frac\{\{\alpha + \sum \nolimits \_\{i = 1\}^k \{\beta \_i x\_\{n - 1\} + \} \sum \nolimits \_\{i = 1\}^k \{\gamma \_i y\_\{n - 1\} \} \}\}\{\{A + \sum \nolimits \_\{j = 1\}^k \{B\_j x\_\{n - j\} + \} \sum \nolimits \_\{j = 1\}^k \{C\_j y\_\{n - j\} \} \}\}, y\_n = \frac\{\{p + \sum \nolimits \_\{i = 1\}^k \{\delta \_i x\_\{n - i\} + \} \sum \nolimits \_\{i = 1\}^k \{\varepsilon \_i y\_\{n - i\} \} \}\}\{\{q + \sum \nolimits \_\{j = 1\}^k \{D\_j x\_\{n - j\} + \} \sum \nolimits \_\{j = 1\}^k \{E\_j y\_\{n - j\} \} \}\} n \in \mathbb \{N\} \] . 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.},
author = {Gabriel Lugo, Frank Palladino},
journal = {Open Mathematics},
keywords = {Difference equation; Systems; Boundedness character; systems; boundedness; rational difference equations},
language = {eng},
number = {6},
pages = {1058-1090},
title = {Some boundedness results for systems of two rational difference equations},
url = {http://eudml.org/doc/269538},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Gabriel Lugo
AU - Frank Palladino
TI - Some boundedness results for systems of two rational difference equations
JO - Open Mathematics
PY - 2010
VL - 8
IS - 6
SP - 1058
EP - 1090
AB - We study k th order systems of two rational difference equations \[ x_n = \frac{{\alpha + \sum \nolimits _{i = 1}^k {\beta _i x_{n - 1} + } \sum \nolimits _{i = 1}^k {\gamma _i y_{n - 1} } }}{{A + \sum \nolimits _{j = 1}^k {B_j x_{n - j} + } \sum \nolimits _{j = 1}^k {C_j y_{n - j} } }}, y_n = \frac{{p + \sum \nolimits _{i = 1}^k {\delta _i x_{n - i} + } \sum \nolimits _{i = 1}^k {\varepsilon _i y_{n - i} } }}{{q + \sum \nolimits _{j = 1}^k {D_j x_{n - j} + } \sum \nolimits _{j = 1}^k {E_j y_{n - j} } }} n \in \mathbb {N} \] . 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.
LA - eng
KW - Difference equation; Systems; Boundedness character; systems; boundedness; rational difference equations
UR - http://eudml.org/doc/269538
ER -