Complete chaotic synchronization and exclusion of mutual Pyragas control in two delay-coupled R\"ossler-type oscillators

Two identical chaotic oscillators that are mutually coupled via time delayed signals show very complex patterns of completely synchronized dynamics including stationary states and periodic as well as chaotic oscillations. We have experimentally observed these synchronized states in delay-coupled electronic circuits and have analyzed their stability by numerical simulations and analytical calculations. We found that the conditions for longitudinal and transversal stability largely exclude each other and prevent e.g. the synchronization of Pyragas-controlled orbits. Most striking is the observation of complete chaotic synchronization for large delay times, which should not be allowed in the given coupling scheme on the background of the actual paradigm.