We present experimental evidence for coexisting periodic attractors in a
semiconductor laser subject to external optical injection. The coexisting
attractors appear after the semiconductor laser has undergone a Hopf
bifurcation from the locked steady state. We consider the single mode rate
equations and derive a third order differential equation for the phase of the
laser field. We then analyze the bifurcation diagram of the time periodic
states in terms of the frequency detuning and the injection rate and show the
existence of multiple periodic attractors.Comment: LaTex, 14 pages, 6 postscript figures include