title: Delayed feedback control of three diffusively coupled Stuart-Landau oscillators: a case study in equivariant Hopf bifurcation.
abstract: The modest aim of this case study is the non-invasive and pattern-selective stabilization of discrete rotating waves ('ponies on a merry-go-round') in a triangle of diffusively coupled Stuart-Landau oscillators. We work in a setting of symmetry-breaking equivariant Hopf bifurcation. Stabilization is achieved by delayed feedback control of Pyragas type, adapted to the selected spatio-temporal symmetry pattern. Pyragas controllability depends on the parameters for the diffusion coupling, the complex control amplitude and phase, the uncontrolled super-/sub-criticality of the individual oscillators and their soft/hard spring characteristics. We mathematically derive explicit conditions for Pyragas control to succeed.
authors: Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, 14195 Berlin, Germany. isabelle.schneider@fu-berlin.de
authors: Isabelle
authors: I
authors: Schneider
keywords: Pyragas control; Stuart–Landau oscillators; equivariant Hopf bifurcation; pattern-selective; time-delayed feedback