On solutions of a system of rational difference equations
Yu Yang, Li Chen and Yong-Guo Shi Received: February 10, 2009;
Accepted: September 25, 2010
Abstract.
In this paper we investigate the system of rational difference
equations
where q is a positive integer with p < q, p \not |
q, p is an odd number and
p ³ 3, both a and b are nonzero real constants and the initial values
x_{-q+1}, x_{-q+2}, . . .
x_{0}, y_{-q+1}, y_{-q+2}, . . ., y_{0} are nonzero real numbers. We
show all real solutions of the system are eventually periodic
with period 2pq (resp. 4pq) when (a/b) = 1
(resp. ^{q}(a/b) = -1), characterize the asymptotic behavior
of the solutions when ^{q}a ³ b, which generalizes
Őzban's results of in [Appl. Math. Comput. 188 (2007), 833-837].
Keywords:
System of difference equations; homogeneous equations of degree one;
eventually periodic solutions.
AMS Subject classification:
Primary: 39A11, 37B20.
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