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The question under which conditions oscillators with slightly differentfrequencies synchronize appears in various settings. We show thatsynchronization can be achieved even for harmonic oscillators that arebilinearly coupled via a purely dissipative interaction. By appropriately tunedgain/loss stable dynamics may be achieved where for the cases studied in thiswork all oscillators are synchronized. These findings are interpreted using thecomplex eigenvalues and eigenvectors of the non-Hermitian matrix describing thedynamics of the system.

Synchronized states in dissipatively coupled harmonic oscillator networks