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Synchronization of a Duffing oscillator with a Van der Pol equation under sinusoidal constraints

Tianyi Liu, Jinjun Fan, Shan Xue


In this paper, the synchronization of a Duffing oscillator with a Van der Pol equation under sinusoidal constraints is investigated through the flow switchability theory of discontinuous dynamical systems. The analytical conditions for the synchronization of the two different dynamical systems are given, and the invariant set of sinusoidal synchronization is obtained based on the analytical conditions. Switching points for appearance and vanishing of the complete and partial synchronization are also developed. For a better understanding of the sinusoidal synchronization, the numerical simulations are carried out to illustrate the analytical conditions of the synchronization. This paper presents a method to illustrate the dynamical system synchronization under special constraints by using the theory of discontinuous dynamical systems. The function synchronization of distinct dynamical systems is very useful for telecommunication synchronization and network security.


Duffing oscillator, Van der Pol equation, synchronization, discontinuous dynamical system, flow switchability.

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