We describe the bifurcation set for a class-$A$ laser with an external injected signal in terms of the amplitude and the frequency of the applied field. We explain the dynamical behavior of this kind of lasers in terms of a Lyapunov potential in the case where such a description is possible. In particular, a full description for the deterministic and nondeterministic dynamics can be given by using the Lyapunov potential for some of the external parameters. Depending also on the value of these parameters, the phase of the electric field drifts with time in the stochastic case.

• Received 14 January 2002

DOI:https://doi.org/10.1103/PhysRevA.66.013808