Synchronization of two low-dimensional Kerr chains

Synchronization of two chaotic low-dimensional chains (α1, α2, α3) and (A1, A2, A3) consisting of Kerr oscillators is studied. The synchronization has been achieved by the parallel coupling of α1 with A1, α2 with A2 and α3 with A3. We want to find whether and when the pairs (α1, A1), (α2, A2) and (α3, A3) synchronize non-simultaneously (three-time synchronism). The problem of synchronization is also studied for a number of couplings between the chains lower than the number of oscillators in a single chain. Both the ring and linear geometry of synchronization is investigated. The presented results suggest a possibility of multi-time synchronism in two coupled high-dimensional chains. It seems very promising for design of some devices for advanced signal processing.