We are concerned with the dynamics and bifurcations of a single-mode semico
nductor laser with optical injection, modeled by three-dimensional rate equ
ations. Key bifurcations, namely saddle-node, Hopf, period-doubling, saddle
-node of limit cycle and torus bifurcations, are followed over a wide range
of injection strengths and detunings for different fixed values of the lin
ewidth enhancement factor alpha. In this way we present, to our best knowle
dge, the most far-reaching overview yet of the dynamics of injected semicon
ductor lasers. Our results compare very well with experimental studies and
tie together information in the literature on different aspects of the beha
vior of optically injected lasers. (C) 1999 Elsevier Science B.V. All right
s reserved.