The periodic character in a higher order difference equation with delays

The aim of this paper is to investigate the global dynamics of the delay nonlinear difference equation yn+1=Ayn−kB+Cyn−lpyn−mq,n=0,1,…, where k, l, and m are positive integers, the parameters A, B, C, p, and q are nonnegative real numbers, and the initial values y−max{k,l,m},…,y−1,y0 are nonnegative real numbers such that the denominator is always positive. Several numerical simulations are provided to support obtained results. Also, our results extend and generalize the known ones.