Pyragas control (named after the physicist Kestutis Pyragas) is a time delayed feedback scheme that aims to stabilize periodic solutions of ordinary differential equations. The feedback scheme preserves periodic orbits with a given period, but drastically changes the dynamics in their neighbourhoods and hence has the potential to make the periodic orbits stable.
In this talk, we explore how Pyragas control can be adapted in the situation where a system and its periodic orbits have `unconventional symmetries’, i.e. in the case where there are relations between the periodic solutions of the system that cannot be described by group equivariance. Guided by examples from network dynamics, we discuss how we can adequately describe such relations, how we can design a Pyragas-like control scheme and what the stabilization properties of this control scheme are. This is based upon joint work in progress with Bob Rink (VU Amsterdam).