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 equationy n + 1 = A y n − kB + C y n − l py n − m q, 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 valuesy − max { k , l , m } , … , y − 1 , y 0are 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.