Abstract: This paper is concerned with the following rational difference equation xn+1=ax_n-bx_n-1+ex²_n/(cX_n+dx_n-1), with the initial conditions x_-1, x₀∈ (0, +∞) and a, b, c, d, e ∈ R⁺. Locally asymptotically stability, global attractively and boundedness character of the equilibrium point of the equation are investigated. Moreover, simulation is shown to support the results.

Key words: global stability, attractively, boundedness, numerical simulation