On the Behavior of Positive Solutions of a Difference Equations System x<sub>n+1</sub>={y<sub>n-2</sub>+y<sub>n-3</sub>}/x<sub>n</sub>, y<sub>n+1</sub>={x<sub>n-2</sub>+x<sub>n-3</sub>}/y<sub>n</sub>

• 作者: Decun Zhang Liying Wang Wenqiang Ji Xiaobao Li
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Difference Equation SYSTEM Monotonicity Periodicity Oscillatory
• 年，卷（期）: 2013,（9）
• 页码范围: 13-18
• 页数: 6页
• 分类号: O1

摘要

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.