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 x"n"+"1=x"n+px"n"-"kx"n+q,n>=0, where the initial conditions x"-"k,...,x"-"1,x"0 are nonnegative, and p,q>0.