On the solutions and behavior of rational systems of diﬀerence equations

Elsayed M. Elsayed; H. S. Gafel

doi:10.5269/bspm.63828

Elsayed M. Elsayed King Abdulaziz University https://orcid.org/0000-0003-0894-8472
H. S. Gafel King Abdulaziz University

DOI: https://doi.org/10.5269/bspm.63828

Abstract

In this paper, we obtain the expressions of the solutions of the following nonlinear systems of difference equations

x_{n+1}=((x_{n-9})/(1+x_{n-9}y_{n-4})), y_{n+1}=((y_{n-9})/(±1±x_{n-4}y_{n-9})),n=0,1,...,

where the initial conditions x₋₉, x₋₈, x₋₇, x₋₆, x₋₅, x₋₄, x₋₃, x₋₂, x₋₁, x₀, y₋₉, y₋₈, y₋₇, y₋₆, y₋₅, y₋₄, y₋₄, y₋₃, y₋₂, y₋₁, y₀ are arbitrary non zero real numbers.

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