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 = [insert ignore into journalissuearticles values(α-y n );/ insert ignore into journalissuearticles values(βy n-1 );] − [insert ignore into journalissuearticles values(γ-y n-1 );/ βy n ] ,   n=0,1,2,..., where the initial conditions  y −1 ,  y 0 are arbitrary positive real numbers such that  y n ≠ 0 for n= −1,0,1,...,  , α, β, γ ε insert ignore into journalissuearticles values(0,∞);  and α > γ. Furthermore we investigate the periodic nature of the mentioned difference equation. Key Words: Difference Equations, Local Stability, Period-two Solutions.