Ukrainian mathematical congress - 2009

Юрій Майстренко (Інститут математики НАН України, Київ, Україна)

Chimera States in Equations with Delay

Yuri L. Maistrenko (Institute of Mathematics and National Scientific Centre for Medical and Biotechnical Research, NAS of Ukraine, Kyiv, Ukraine),
Oleh E. Omel'chenko (Institute of Mathematics, NAS of Ukraine, Kiev, Ukraine and Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany),
Peter A. Tass (Research Centre Juelich, Germany)

We propose a new mechanism based on the spatially modulated delayed feedback for generation of chimera states — remarkable spatiotemporal patterns in which coherence coexists with incoherence. Combining theoretical and numerical approaches we systematically describe the relationship between the parameters of the delayed feedback on the one side, and the properties of the chimera states on the other side. The general rules how to effectively control and manipulate the chimera states are formulated [1]

[1] Oleh E.Omelchenko, Yuri L.Maistrenko, and Peter A.Tass. Chimera states: the natural link between coherence and incoherence. Physical Review Letters, Vol. 100 (2008), 044105.