On the Behavior of Positive Solutions of a Difference Equations System x_n+1={y_n-2+y_n-3}/x_n, y_n+1={x_n-2+x_n-3}/y_n

Decun Zhang, Wenqiang Ji, Liying Wang, Xiaobao Li

Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, Yantai, China.

DOI: 10.4236/am.2013.49A003                

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:

x_n+1={y_n-2+y_n-3}/x_n, y_n+1={x_n-2+x_n-3}/y_n , n=o, 1 ...* Where x_i, y_i ∈（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.

Keywords

Difference Equation; System; Monotonicity; Periodicity; Oscillatory

Conflicts of Interest

The authors declare no conflicts of interest.

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