Periodic model containing coupled subsystems with different types of oscillations

The periodic model containing coupled subsystems (MCCS) is considered. MCCS decouples into systems of autonomic ordinary differential equations when the coupling between the subsystems vanishes. The subsystems are supposed to admit of various types of non-degenerate single-frequency oscillations. For the MCCS the following problems are solved: existence of oscillations and their stability, natural stabilization of oscillations by smooth time-periodic coupling controls. An example is given.