Synchronization and multi-frequency oscillations in the chain of phase oscillators

The problem of the dynamics of phase oscillators is discussed with an increasing their numbers. We discuss the organization of the parameters plane responsible for the frequency detunings of the oscillators and amplitude of the dissipative coupled. The region of complete synchronization, quasi-periodic oscillations of different dimension and chaos are are observed. We discuss the changing of the synchronization picture with an increasing of the number of oscillators in the chain. We use the method of charts of Lyapunov exponents and modification of the method of charts of dynamical regimes visualized two-frequency resonant tori of different types.