Controlled phase synchronization in oscillatory networks

We propose a method of automatic phase locking of regular and chaotic non-identical oscillations. Our approach is based on the principles of feedback control which implicitly play the role of an internal self-organization mechanism in the huge variety of natural oscillators and which explicitly serve as the basis of phase locked loops. This way phase synchronization via phase locking is achieved for very low coupling and this is demonstrated for several examples: (1) two coupled regular oscillators, (2) coupled regular and chaotic oscillators, (3) two coupled chaotic oscillators, (4) ensembles of locally coupled regular oscillators, (5) ensembles of locally coupled chaotic oscillators, and (6) ensembles of globally coupled chaotic oscillators.