Consideration was given to the model containing coupled subsystems (MCCS). With
no connection between the subsystems, the MCCS falls down into independent subsystems, that
is, systems of autonomous ordinary differential equations. MCCS with cycles in the subsystems
were examined. For the autonomous MCCS, conditions were established for cycles and their
stability, and a cycle stabilization by the control explicitly independent of time was proposed.
For the periodic MCCS, generation of isolated periodic solutions was proved, and the problem
of their stability and stabilization was solved.