Automatic control of phase synchronization in coupled complex oscillators

We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, our approach supposes the existence of a special controller, whose input is given by a quadratic form of the coordinates of the individual systems and its output is a result of the application of a linear differential operator. Using several examples we demonstrate the effectiveness of our approach to achieve controlled phase synchronization.