Global attractivity in a quadratic-linear rational difference equation with delay

Abstract

We investigate the global behaviour of non-negative solutions of the following rational difference equation with arbitrary delay and quadratic terms in its numerator: where all coefficients are non-negative and and γ>0. In this case, the origin is the only non-negative fixed point and we establish the asymptotic stability of the origin relative to an invariant set and behaviour of positive solutions outside that invariant set. We also state conditions implying that the invariant set is , i.e. the origin is a global attractor of all non-negative solutions.