Controlling Phase Synchronization in Oscillatory Networks

In this chapter we present an automatic control method of phase locking of regular and chaotic nonidentical oscillations, when all subsystems interact by a feedback [332]. This method is basing on the well-known principle of feedback control which takes place in nature and is successfully used in engineering. Considering the models of coupled systems in biology, neuroscience, and ecology one can see that in many of them the coupling between interacting elements is nonlinear, and usually has the form of quadratic functions of the subsystem variables. Such a coupling serves as the basis of an internal self-organization mechanism leading to a balanced motion in these systems. Synaptically coupled neurons [342, 343], phase transitions in human hand movement [344], ecological systems [339], or spinal generators of locomotion [345], are only some well-known examples of balanced cooperative oscillatory motion, caused by such a nonlinear coupling. In engineering, nonlinear coupling, is used, for example, in coupled lasers [333, 334] or phase-locked loops (PLL) [57] (see also Sect. 2.5).