Synchronization between Coupled Oscillators: An Experimental Approach

Rijlaarsdam, David; Pogromsky, Alexander Yu.; Nijmeijer, Henk

doi:10.1142/9789814282321_0010

Cited by 5 publications

(8 citation statements)

References 10 publications

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“…In Section 3, it has been shown that this is also true for the case where the metronomes are replaced by two self-driven discontinuous mass-spring-damper oscillators. Obviously, this result suggests that this may be true for other second order nonlinear oscillators [19,22,23].…”

Section: Discussionmentioning

confidence: 72%

“…Clearly, in closed loop, the dynamics of Eq. (1) with controllers (18)- (19) coincide with the dynamics of Eq. (9).…”

Section: Adjustment Of the Experimental Setup To Mimic Huygens' Systemmentioning

confidence: 86%

“…(1) (1) have been obtained experimentally and presented in [19]. Since in an experiment only positions are measured, the state vector [x 1ẋ1 x 2ẋ2 x 3ẋ3 ] T is fully reconstructed by using a robust observer as presented in [20].…”

Section: Experimental Setup and Model Descriptionmentioning

confidence: 99%

“…Therefore, the experimental setup has been "converted" into the classical Huygens' model. Note that in the ideal case, a perfect cancellation of the original dynamics (1) is achieved by using the first part of (18) and (19). However, in practice, the dynamics are not perfectly known and therefore a perfect cancellation of the original dynamics (1) cannot be achieved.…”

Section: Adjustment Of the Experimental Setup To Mimic Huygens' Systemmentioning

confidence: 99%

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An experimental study on synchronization of nonlinear oscillators with Huygens' coupling

Ramirez

Fey

Nijmeijer

2012

NOLTA

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Abstract:In this experimental study, phase synchronization is studied in pairs of nonlinear oscillators coupled through a movable support. In particular, the dynamics of two discontinuous mass-spring-damper oscillators and the dynamics of the classical Huygens' pendulum clocks are considered. In both systems the individual oscillators are self-sustained. It is shown that in both cases, the oscillators exhibit in-phase and anti-phase synchronization. All experiments are executed on a new experimental setup consisting of two controllable mass-spring-damper oscillators coupled through an elastically supported rigid bar. The results suggest, that the synchronized motion observed by Christiaan Huygens around 1650 in a pair of pendulum clocks mounted on a flexible support, in many cases can also be observed when the pendulum clocks are replaced by other self-sustained nonlinear oscillators.

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Section: Discussionmentioning

confidence: 72%

“…Clearly, in closed loop, the dynamics of Eq. (1) with controllers (18)- (19) coincide with the dynamics of Eq. (9).…”

Section: Adjustment Of the Experimental Setup To Mimic Huygens' Systemmentioning

confidence: 86%

Section: Experimental Setup and Model Descriptionmentioning

confidence: 99%

Section: Adjustment Of the Experimental Setup To Mimic Huygens' Systemmentioning

confidence: 99%

See 2 more Smart Citations

An experimental study on synchronization of nonlinear oscillators with Huygens' coupling

Ramirez

Fey

Nijmeijer

2012

NOLTA

Self Cite

View full text Add to dashboard Cite

show abstract

“…This type of coupling arises in various areas of science arranging from physiology 16,17 and neuroscience [18][19][20][21][22] to electrical systems 23,24 and mechanical engineering. [25][26][27][28] In addition, we allow the coupling to contain time-delays, which can arise due to finite propagation speed of information and/or the time it takes to make decisions, cf. Ref.…”

Section: Introductionmentioning

confidence: 99%

Partial synchronization in diffusively time-delay coupled oscillator networks

Steur

Oguchi

Leeuwen

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study networks of diffusively time-delay coupled oscillatory units and we show that networks with certain symmetries can exhibit a form of incomplete synchronization called partial synchronization. We present conditions for the existence and stability of partial synchronization modes in networks of oscillatory units that satisfy a semipassivity property and have convergent internal dynamics. In the study of synchronization in oscillator networks where coupling is diffusive and allows for time-delays, the focus is on deriving conditions that guarantee synchronization of all units in the network. We considered the question what happens if full synchronization cannot be achieved. Will there be no collective behavior at all or might it be possible that partial synchronization occurs, i.e., that some, but not all, units synchronize? We show that if a network contains certain symmetries, then these symmetries identify modes of partial synchronization. We present conditions for the existence and stability of partial synchronization modes in networks of diffusive time-delay coupled oscillatory units. The results are supported by numerical simulations in several networks of diffusively time-delay coupled neural Hindmarsh-Rose oscillators.

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