Dynamics of the difference equation xn+1=xn+pxn−kxn+q

We study the invariant interval, the character of semicycles, the global stability, and the boundedness of the difference equation xn+1=xn+pxn−kxn+q,n≥0, where the initial conditions x−k,…,x−1,x0x−k,…,x−1,x0 are nonnegative, and p,q>0p,q>0.