Global attractivity of a higher-order nonlinear difference equation

The main goal of this paper is to investigate the locally asymptotically stable, period-two solutions, invariant intervals and global attractivity of all negative solutions of the nonlinear difference equationxn+1=1-xnA+xn-k,n=0,1,…,where A∈(-∞,-1),k is a positive integer and initial conditions x-k,…,x0∈(-∞,0]. It is shown that the unique negative equilibrium of the equation is a global attractor with a basin that depends on certain conditions of the coefficient.