In this paper we establish conditions which ensure the nonexistence of 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 nonexistence of limit cycles in interconnected systems.
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Skar et al. (1981) studied this question.
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