ABSTRACT
This chapter considers a model for a host laser (usually a power laser) with the signal of a (low-power) laser injected in the cavity of the host. Such an experiment usually has the goal of forcing a power laser to work at the frequency of the weak (injected) laser and is usually referred as ‘locking’ of the signals. Problems involving singular perturbations are of importance and will play an increasingly relevant role as the field moves towards considering questions involving spatially extended systems described by partial differential equations. Finally a word about the effect of the neglected terms. The terms neglected are of two kinds: time independent and time dependent. In the first case, the terms will modify the exact values of the transitions between different kinds of flow. The time-dependent terms have the potential ability of making transverse homoclinic connections of the homoclinic cycles associated with the Hamiltonian cases by the Melnikov mechanism.
