On the Dynamics of the Recursive Sequence

Abstract

Our aim in this paper is to investigate the local stability of the positive solutions of the difference equationyn+1= [(α-yn)/ (βyn-1)] − [(γ-yn-1)/ βyn ] , n=0,1,2,...,where the initial conditions y−1 , y0 are arbitrary positive real numbers such that yn ≠ 0 for n= −1,0,1,..., , α, β, γ ε (0,∞) and α > γ. Furthermore we investigate the periodic nature of the mentioned difference equation.Key Words: Difference Equations, Local Stability, Period-two Solutions.