On the Dynamics of the Recursive Sequence

Our aim in this paper is to investigate the local stability of the positive solutions of the difference equation y_n+1= (α-y_n)/(βy_n-1) - (ϒ-y_n-1)/(βy_n), n = 0,1,2,..., where the initial conditions y−1 , y0 are arbitrary positive real numbers such that y_n ≠ 0 for n = −1,0,1,..., , α,β, γ∈(0,∞) and α γ . Furthermore we investigate the periodic nature of the mentioned difference equation.