Synchronization of two coupled multimode oscillators with time-delayed feedback

• We consider two coupled oscillators with time-delayed feedback.
• The mechanisms of transition from beating to synchronous regime are studied.
• Periodical zones of amplitude death and “broadband synchronization” are detected.
• Results of numerical simulation completely agree with analytically obtained formulas.

Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires many new features not inherent to finite-dimensional ones. A picture of oscillation modes in cases of identical and non-identical coupled oscillators is studied in detail. Periodical structure of amplitude death and “broadband synchronization” zones is investigated. Such a behavior occurs due to the resonances between different modes of the infinite-dimensional system with time delay.