Synchronization of weakly nonlinear oscillators with Huygens' coupling

J. Pena Ramirez; R.H.B. Fey; H. Nijmeijer

doi:10.1063/1.4816360

Synchronization of weakly nonlinear oscillators with Huygens' coupling

J. Pena Ramirez, R.H.B. Fey, H. Nijmeijer

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Abstract

In this paper, the occurrence of synchronization in pairs of weakly nonlinear selfsustained oscillators that interact via Huygens’ coupling, i.e. a suspended rigid bar, is treated. In the analysis, a generalized version of the classical Huygens’ experiment of synchronization of two coupled pendulum clocks is considered, in which the clocks are replaced by arbitrary self-sustained oscillators. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the Poincar´e method. The obtained results are supported by computer simulations and experiments conducted on a dedicated experimental platform. It is demonstrated that the mass of the coupling bar is an important parameter with respect to the limit synchronous behaviour in the oscillators.

Original language	English
Article number	033118
Pages (from-to)	033118-1/12
Number of pages	12
Journal	Chaos
Volume	23
Issue number	3
DOIs	https://doi.org/10.1063/1.4816360
Publication status	Published - 2013

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abstract = "In this paper, the occurrence of synchronization in pairs of weakly nonlinear selfsustained oscillators that interact via Huygens{\textquoteright} coupling, i.e. a suspended rigid bar, is treated. In the analysis, a generalized version of the classical Huygens{\textquoteright} experiment of synchronization of two coupled pendulum clocks is considered, in which the clocks are replaced by arbitrary self-sustained oscillators. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the Poincar´e method. The obtained results are supported by computer simulations and experiments conducted on a dedicated experimental platform. It is demonstrated that the mass of the coupling bar is an important parameter with respect to the limit synchronous behaviour in the oscillators.",

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AU - Fey, R.H.B.

AU - Nijmeijer, H.

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N2 - In this paper, the occurrence of synchronization in pairs of weakly nonlinear selfsustained oscillators that interact via Huygens’ coupling, i.e. a suspended rigid bar, is treated. In the analysis, a generalized version of the classical Huygens’ experiment of synchronization of two coupled pendulum clocks is considered, in which the clocks are replaced by arbitrary self-sustained oscillators. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the Poincar´e method. The obtained results are supported by computer simulations and experiments conducted on a dedicated experimental platform. It is demonstrated that the mass of the coupling bar is an important parameter with respect to the limit synchronous behaviour in the oscillators.

AB - In this paper, the occurrence of synchronization in pairs of weakly nonlinear selfsustained oscillators that interact via Huygens’ coupling, i.e. a suspended rigid bar, is treated. In the analysis, a generalized version of the classical Huygens’ experiment of synchronization of two coupled pendulum clocks is considered, in which the clocks are replaced by arbitrary self-sustained oscillators. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the Poincar´e method. The obtained results are supported by computer simulations and experiments conducted on a dedicated experimental platform. It is demonstrated that the mass of the coupling bar is an important parameter with respect to the limit synchronous behaviour in the oscillators.

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