Dynamics of solitary waves generated by subcritical instability under the action of delayed feedback control

We consider the influence of a global delayed feedback control which acts on a system governed by a subcritical Ginzburg–Landau equation. The method based on a variational principle is applied for the derivation of a low-dimensional evolution model. In the framework of this model a one-pulse solution is found, and its linear and nonlinear stability analysis is carried out. The existence region for a stable time-periodic pulse solution is found between the boundaries in the parameter space corresponding to a Hopf bifurcation and a saddle-node bifurcation. The obtained results are compared with the results of an analytical linear theory and direct numerical simulations of the original problem.