On the Dynamics of the Nonlinear Difference Equation <i>xn</I>+1 = Α Plus Β<i>xn</I>-1 + <i>xn</I>-1

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 x(n+1) = alpha + beta x(n-1) + x(n-1)/x(n), n = 0,1,... are investigated where alpha is an element of [0, infinity), beta is an element of [0, 1) and the initial conditions x(-1) and x(0) are arbitrary positive real numbers. The paper concludes with some numerical examples to illustrate the theoretical results.