Time-delayed feedback control of spatially extended systems
- When?
- Friday 16 October 2009, 16:00 to 17:00
- Where?
- 22AA04
- Open to:
- Staff, Students
Speaker: Dr Yuliya Kyrychko (Bristol)
Abstract: Time delayed feedback control (TDFC) is an efficient tool widely used to stabilize unstable steady states and periodic orbits as well as chaotic motion. This type of control is based on the difference of system's variables at the current moment and their values sometime ago.
I will introduce the concept of the TDFC, and show some examples where it has been successfully implemented to control unstable steady states/periodic orbits. I will present results on TDFC of spatio-temporal chaos on the example of the Gray-Scott system. Different types of control schemes are investigated, including single-species, diagonal and mixed control. This approach helps to unveil different dynamical regimes, which arise from chaotic state or from travelling waves. In the case of spatio-temporal chaos, the control can either stabilize uniform steady states or lead to bistability between a trivial steady state and a propagating travelling wave. Furthermore, when the basic state is a stable travelling pulse, the control is able to advance stationary Turing patterns, or yield the above-mentioned bistability regime. In each case, the stability boundary is found in the parameter space of the control strength and the time delay, and numerical simulations suggest that diagonal control fails to stabilize spatio-temporal chaos.
