TITLE:
On the Behavior of Positive Solutions of a Difference Equations System xn+1={yn-2+yn-3}/xn, yn+1={xn-2+xn-3}/yn
AUTHORS:
Decun Zhang, Wenqiang Ji, Liying Wang, Xiaobao Li
KEYWORDS:
Difference Equation; System; Monotonicity; Periodicity; Oscillatory
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.9A,
September
6,
2013
ABSTRACT:
Motivated by an open problem in the literature “Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture”, we introduce a difference equation system:
xn+1={yn-2+yn-3}/xn, yn+1={xn-2+xn-3}/yn , n=o, 1 ...* Where xi, yi ∈(0, ∞), i=-3, -2, -1, 0.
We try to find out some conditions such that the solution of system converges to periodic solution. This model can be applied to the two species competition and population biology.