Abstract:
In this paper we show that the system of difference equations
xn = ayn−k +
dyn−kxn−(k+l)
bxn−(k+l) + cyn−l
, yn = αxn−k +
δxn−kyn−(k+l)
βyn−(k+l) + γxn−l
,
where n ∈ N0, k and l are positive integers, the parameters a, b, c, d, α, β, γ, δ are real
numbers and the initial values x−j , y−j , j = 1, k + l, are real numbers, can be solved
in the closed form. We also determine the asymptotic behavior of solutions for the case
l = 1 and describe the forbidden set of the initial values using the obtained formulas. Our
obtained results significantly extend and develop some recent results in the literature.
