Synchronization and multi-frequency oscillations in the low-dimensional chain of the self-oscillators

The problem of the dynamics of the coupled phase oscillators as the number of oscillators in the chain increases is considered. The organization of the parameter space is discussed. The regions of complete synchronization, quasi-periodic regimes of different dimensions and chaos are identified. We discuss transformation of the domains of different dynamics as the number of oscillators grows. Features of the transition from the phase model to the original system are discussed for the case of coupled van der Pol oscillators. Keywords: synchronization, phase oscillators, quasi-periodic dynamics, chaos.