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Synchronization of two different dynamical systems under sinusoidal constraint. (English) Zbl 1463.37025

Summary: 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.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D06 Synchronization of solutions to ordinary differential equations
34A36 Discontinuous ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K40 Forced motions for nonlinear problems in mechanics
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