Front dynamics in a delayed-feedback system with external forcing

A scalar nonlinear delay-differential equation of the kind arising in optically bistable systems is reduced, in some physically relevant limit, to a partial differential equation first, and then to a system of ordinary differential equations. These simplified equations are studied analytically. We describe the continuous deformation of periodic solutions from sine waves to square waves away from the oscillation threshold, and determine their stability. We also study the effect of a weak periodic modulation. It is found that a resonant forcing can stabilize a very large number of oscillation modes taking the form of square waves with missing front pairs.