On existence and nonexistence of limit cycles in interconnected systems

In this paper we establish conditions which ensure the existence and the nonexistence of self-excited oscillations (limit cycles) in complex dynamical systems. We consider those types of systems which can be viewed as an interconnection of several simpler subsystems. Our results are phrased in terms of the qualitative properties of the free subsystems and in terms of the system interconnecting structure and they yield easily interpreted graphical criteria for the existence and nonexistence of limit cycles in interconnected systems. The applicability of the main result is demonstrated by means of a specific example.