title: Bifurcation to fronts due to delay.
abstract: The stability of a steady-state front (kink) subject to a time-delayed feedback control (TDFC) is examined in detail. TDFC is based on the use of the difference between system variables at the current moment of time and their values at some time in the past. We first show that there exists a bifurcation to a moving front. We then investigate the limit of large delays but weak feedback and obtain a global bifurcation diagram for the propagation speed. Finally, we examine the case of a two-dimensional front with radial symmetry and determine the critical radius above which propagation is possible.
authors.affiliation: Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Campus Plaine, CP 231, 1050 Bruxelles, Belgium. terneux@ulb.ac.be
authors.forename: T
authors.initials: T
authors.lastname: Erneux
authors.forename: G
authors.initials: G
authors.lastname: Kozyreff
authors.forename: M
authors.initials: M
authors.lastname: Tlidi
mesh_terms: D005246:Feedback; D055641:Mathematical Concepts; D017711:Nonlinear Dynamics; D013598:Systems Theory; D013997:Time Factors