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Research articles

ScienceAsia 41 (2015): 350-356 |doi: 10.2306/scienceasia1513-1874.2015.41.350

On the dynamics of the nonlinear difference equation xn+1=α+βxn−1+xn−1/xn

Aycan Aksoy, Mehmet Turan*

ABSTRACT:     The boundedness and semi-cycle analysis of positive solutions, existence of period-2 solutions, and local and global asymptotic stability of the recursive sequence xn+1=α+βxn−1+xn−1/xn, n=0,1,... are investigated where α∈[0,∞), β∈[0,1) and the initial conditions x−1 and x0 are arbitrary positive real numbers. The paper concludes with some numerical examples to illustrate the theoretical results.

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Atilim University, Department of Mathematics, Incek 06836, Ankara, Turkey

* Corresponding author, E-mail: mehmet.turan@atilim.edu.tr

Received 18 Feb 2015, Accepted 12 Oct 2015