Chimera states induced by spatially modulated delayed feedback

Recently, we have presented spatially modulated delayed feedback as a novel mechanism, which generically generates chimera states, remarkable spatiotemporal patterns in which coherence coexists with incoherence [O. E. Omel'chenko et al., Phys. Rev. Lett. 100, 044105 (2008)]. Remarkably, such chimera states serve as a natural link between completely coherent states and completely incoherent states. So far, we have studied this mechanism with a self-consistency-based numerical analysis only. In contrast, in this paper we perform a thorough dynamical description and, in particular, a stability analysis of the emerging chimera states. For this, we apply a recently developed reduction procedure [A. Pikovsky and M. Rosenblum, Phys. Rev. Lett. 101, 264103 (2008)]. By combining analytical and numerical approaches, we systematically describe the relationship between the parameters of the delayed feedback on one hand and the properties of the chimera states on the other hand. We provide the general rules for an effective control and manipulation of the chimera states.