Synchronization of Two Different Dynamical Systems under Sinusoidal Constraint

This paper discusses the synchronization of the Van der Pol equation with a pendulum under the sinusoidal constraint through the theory of discontinuous dynamical systems. The analytical conditions for the sinusoidal synchronization of the Van der Pol equation with a periodically forced pendulum are developed. With the conditions, the sinusoidal synchronizations of the two systems are discussed. Switching points for appearance and vanishing of the partial synchronization are developed.

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