On the Problem of Synchronization of Identical Dynamical Systems: The Huygens’s Clocks

Dilão, Rui

doi:10.1007/978-0-387-95857-6_10

Cited by 8 publications

(19 citation statements)

References 11 publications

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“…However, Czolczynski et al [5] later confirmed co-existence of both regimes experimentally using modern clocks with non-impulsive escapements. Numerical simulations in [6,7] also show co-existence for some parameter values. The common trait in all three cases is that the escapements involved do not have an engagement threshold.…”

Section: Introductionmentioning

confidence: 74%

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Synchronization of Huygens' clocks and the Poincaré method

Jovanović

Koshkin

2012

Journal of Sound and Vibration

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We study two models of connected pendulum clocks synchronizing their oscillations, a phenomenon originally observed by Huygens. The oscillation angles are assumed to be small so that the pendulums are modeled by harmonic oscillators, clock escapements are modeled by the van der Pol terms. The mass ratio of the pendulum bobs to their casings is taken as a small parameter. Analytic conditions for existence and stability of synchronization regimes, and analytic expressions for their stable amplitudes and period corrections are derived using the Poincaré theorem on existence of periodic solutions in autonomous quasi-linear systems. The anti-phase regime always exists and is stable under variation of the system parameters. The in-phase regime may exist and be stable, exist and be unstable, or not exist at all depending on parameter values. As the damping in the frame connecting the clocks is increased the in-phase stable amplitude and period are decreasing until the regime first destabilizes and then disappears. The results are most complete for the traditional three degrees of freedom model, where the clock casings and the frame are consolidated into a single mass.

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Section: Introductionmentioning

confidence: 74%

“…The corresponding linear generating system (see Appendix for the terminology) is obtained by setting µ = 0 in (6). Poincaré theorem gives sufficient conditions for existence and stability of periodic solutions to the original non-linear system that converge to periodic solutions of the generating system when µ → 0.…”

Section: Small Damping In the Framementioning

confidence: 99%

Synchronization of Huygens' clocks and the Poincaré method

Jovanović

Koshkin

2012

Journal of Sound and Vibration

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“…enforces the synchronization objective given in Eq. (12). Furthermore, if conditions (36) are satisfied, then the synchronous solution (12) is locally asymptotically stable.…”

Section: Stability Of the Desired Synchronous Solutionmentioning

confidence: 99%

“…Likewise, there are works, see, e.g., [10][11][12][13][14], in which it has been demonstrated that the damping in the system has a strong influence on the type of synchronization: for relatively large damping the pendula tend to synchronize in anti-phase, whereas for relatively small damping the pendula 'prefer' to synchronize in-phase.…”

Section: Literature Reviewmentioning

confidence: 99%

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Enforcing synchronization in oscillators with Huygens’ coupling via feed-forward control

Ramirez

Nijmeijer

2019

Nonlinear Dyn

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A Nanoscale Bistable Resistor for an Oscillatory Neural Network

Yun,

Han,

Choi

2024

Nano Lett.

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Coupled oscillators construct an oscillatory neural network (ONN) by mimicking the interactions among neurons in the human brain. This work demonstrates a fully CMOS-based oscillator consisting of a bistable resistor (biristor), which shares a structure identical with that of a metal-oxide-semiconductor fieldeffect transistor, except for the use of a gate electrode. The biristorbased oscillator (birillator) generates oscillating voltage signals in the form of spikes due to a single transistor latch phenomenon. When two birillators are connected with a coupling capacitor, they become synchronized with a phase difference of 180°. These coupled oscillation characteristics are experimentally investigated for an ONN. As practical applications of the ONN with coupled birillators, edge detection and vertex coloring are conducted by encoding information into phase differences between them. The proposed fully CMOS-based birillators are advantageous for low power consumption, high CMOS compatibility, and a compact footprint area.

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On the Problem of Synchronization of Identical Dynamical Systems: The Huygens’s Clocks

Cited by 8 publications

References 11 publications

Synchronization of Huygens' clocks and the Poincaré method

Synchronization of Huygens' clocks and the Poincaré method

Enforcing synchronization in oscillators with Huygens’ coupling via feed-forward control

A Nanoscale Bistable Resistor for an Oscillatory Neural Network

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