Low-dimensional description of pulses under the action of global feedback control (Q2896311)

The influence of a global feedback control which acts on a system governed by a subcritical Ginzburg-Landau equation is considered. The method based on a variational principle is applied for the derivation of low-dimensional evolution models. In the process, the authors construct a finite-dimensional model for the description of the indirect interaction of pulses stabilized by the active control. The analysis of this model demonstrates that the replacement of the original delay partial differential equation (PDE) by an approximate delay ordinary differential equation (ODE) obtained by means of a modified variational approach represents a ``cheap'' and rather precise method for studying the stability and nonlinear dynamics of localized structures under the action of a delayed feedback control. Using a delay-ODE model allows the authors to find the oscillatory stability boundary of pulses and to reveal the existence of several new dynamical regimes. Some of new regimes similar to those predicted by the theoretical model are obtained by means of the direct simulation of the original delay-PDE.