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We present a systematic approach to identify the similarities and differences between a chaotic system with delayed feedback and two mutually delay-coupled systems. We consider the general case in which the coupled systems are either unsynchronized or in a generally synchronized state, in contrast to the mostly studied case of identical synchronization. We construct a new time-series for each of the two coupling schemes, respectively, and present analytic evidence and numerical confirmation that these two constructed time-series are statistically equivalent. From the construction, it then follows that the distribution of time-series segments that are small compared to the overall delay in the system is independent of the value of the delay and of the coupling scheme. By focusing on numerical simulations of delay-coupled chaotic lasers, we present a practical example of our findings. © 2013 AIP Publishing LLC.This work was supported by the MICINN (Spain), Comunitat Autònoma de les Illes Balears, FEDER, and European Commission under Projects TEC2012-36335 (TRIPHOP), TEC2009-14101 (DeCoDicA), FIS2007-60237 (FISICOS), 0200950I190 (Proyecto Intramurales Especiales), Grups Competitius, and EC FP7 Project PHOCUS under Grant No. 240763. V.F. acknowledges financial support from the German Academic Exchange Service (DAAD).Peer reviewe

Relation between delayed feedback and delay-coupled systems and its application to chaotic lasers