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Development of Synchronization Theory

These two problems remain fundamental in the classic theory of synchronization: the first one is on the behavior of oscillatory systems driven by a periodical force. The second focuses on the interaction between two coupled oscillatory systems. Both cases give a plethora of dynamical phenomena that exist at different values of control parameters which can either the amplitude and the frequency of the external force, or the coupling strength, respectively. In terms of the theory of dynamical systems, the problem in question sounds as follows: find a synchronization region in the parameter space that corresponds to the existence of a stable periodic orbit, and describe the ways synchronization is lost after crossing the its boundaries. Let an autonomous system