Construction of a stable cycle in weakly coupled identical systems

Consideration was given to a dynamic model containing weakly coupled identical subsystems. The subsystem was assumed to admit a family of periodic solutions where the period is a monotonic function of one parameter. Requirements on the coupling under which the model has an asymptotic orbital stable cycle were established. The problem of stabilization of the model oscillations by a small smooth autonomous coupling control was solved using the results obtained. The system of two coupled conservative systems with one degree of freedom was considered individually.