We perform a detailed study of multistable behaviour in an optically inject
ed semiconductor laser modeled by single-mode three-dimensional rate equati
ons. It turns out that there is a wealth of regions of bi- and multistabili
ty associated with bifurcations of periodic orbits - in the plane of inject
ion strength and injection detuning. We follow such bifurcations over a wid
e range of parameters, which reveals different mechanisms for multistabilit
y in the system. In this way, we find, among others, the coexistence of two
different periodic orbits with a chaotic attractor. Our results open new p
ossibilities for optical switching between several different outputs of the
laser. (C) 2000 Elsevier Science B.V. All rights reserved.