With the help of time-dependent solutions, their power spectra, Poincaré maps, and the complete set of Lyapunov exponents, we have carried out a detailed investigation of the bifurcation routes of three attractors in a single-mode model of a laser with injected signal. In addition to a sequence of ordinary period-doubling bifurcations leading to chaos, we have observed subcritical and supercritical Hopf bifurcations of limit cycles. We have also observed the sudden disappearance of trajectories due to the coalescence of a pair of stable and unstable tori and the possible collision of a limit cycle with an unstable torus.

• Received 29 May 1984

DOI:https://doi.org/10.1103/PhysRevA.31.354