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.