How carrier memory enters the Haus master equation of mode-locking.

We present a generalization of the Haus master equation in which a dynamical boundary condition allows to describe complex pulse trains, such as the -switched and harmonic transitions of passive mode-locking, as well as the weak interactions between localized states. As an example, we investigate the role of group velocity dispersion on the stability boundaries of the -switched regime and compare our results with that of a time-delayed system.