Experimental and numerical study on the basin stability of the coupled metronomes

Wu, Ye; Song, Zhiwen; Liu, W.; Jia, Jing; Xiao, Jinghua

doi:10.1140/epjst/e2014-02135-9

Cited by 9 publications

(12 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many researches have shown that when the coupling strength gradually changes between coupled oscillators, there exists a threshold value 30–34 for the transition of synchronization states, or the basin stability of coherent states changes along with the change of coupling strength 35 . Considering the experiments of two identical oscillators, we might intuitively arrive at a conclusion that the coupling strength should decay along with the augmentation of distance between them.…”

Section: Resultsmentioning

confidence: 99%

Frequency and Phase Characteristics of Candle Flame Oscillation

Chen

Guo

Jia

et al. 2019

Sci Rep

View full text Add to dashboard Cite

The combustion of candles exhibits a variety of dynamical behaviors. Binding several candles together will result in flickering of candle flames, which is generally described as a nonlinear oscillator. The impact on the frequency of the flame by several factors, such as the arrangement, the number and the asymmetry of the oscillators, is discussed. Experimental results show that the frequency gradually decreases as the number of candles increases in the case of an isolated oscillator, while alternation between the in-phase and the anti-phase synchronization appears in a coupled system of two oscillators. Moreover, envelopes in the amplitude of the oscillatory luminance are displayed when candles are coupled asymmetrically. Since the coupling between oscillators is dominated by thermal radiation, a “overlapped peaks model” is proposed to phenomenologically explain the relationship between temperature distribution, coupling strength and the collective behavior in coupled system of candle oscillators in both symmetric and asymmetric cases.

show abstract

Section: Resultsmentioning

confidence: 99%

Frequency and Phase Characteristics of Candle Flame Oscillation

Chen

Guo

Jia

et al. 2019

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Several sensors are set up on the rotating axis. The sensors record the data of the rotating angle of the rotating axis and the horizontal displacement of the slider, and then transmits those data to the computer for further analysis (Wu et al, 2014). The corresponding experimental parameters are set as follows.…”

Section: Methodsmentioning

confidence: 99%

Experimental study on amplitude-frequency characteristic and basin stability of horizontally driven pendulum

Jia¹,

Wu²,

Liu³

et al. 2016

jtam

View full text Add to dashboard Cite

In this article, an inverted pendulum system is set up to explore the dynamics of a horizontally driven pendulum which exhibits a great variety of dynamical behavior and appears in a wide range of applications in the field of engineering. The facility is efficient to experimentally explore two kinds of coexisting movement patterns in the horizontally driven pendulum, i.e. in-phase and anti-phase patterns between the angular velocity of the pendulum rod and the direction of the driving forces. Theoretical analysis is applied to reveal the regimes of the coexistence of the two movement patterns, which is promising to control the system to a desired pattern.

show abstract

“…The phenomenon depicted in figure 5(b) is in consistent with the finding in Refs. [15,21], where it is shown that the basin of APS is enlarged by increasing c x slightly. Figure 5(a) suggests that the basin of APS is increased at the cost of decreased synchronization precision.…”

Section: Experimental Studymentioning

confidence: 98%

“…By the theoretical model proposed by Pantaleone, Ulrichs et al studied numerically the synchronization of coupled metronomes, and pointed out that APS is always unstable and existing only in the transient processes [12]. Wu et al studied the attracting basin of APS in the phase space and found that, by adjusting slightly the friction between the base and its support, the basin can be significantly enlarged, making APS observable for the general initial conditions [15,21]. Despite the extensive studies on pendulum synchronization, the "odd sympathy" discovered by Huygens remains as a puzzle to researchers: Did Huygens generate APS by luck?…”

Section: Introductionmentioning

confidence: 99%

Huygens’ synchronization experiment revisited: luck or skill?

Jiao¹,

Wang²,

Yu³

et al. 2018

Eur. J. Phys.

View full text Add to dashboard Cite

353 years ago, in a letter to the Royal Society of London, Christiaan Huygens described "an odd kind of sympathy" between two pendulums mounted side by side on a wooden beam, which inspired the modern studies of synchronization in coupled nonlinear oscillators. Despite the blooming of synchronization study in a variety of disciplines, the original phenomenon described by Huygens remains a puzzle to researchers. Here, by placing two mechanical metronomes on top of a freely moving plastic board, we revisit the synchronization experiment conducted by Huygens. Experimental results show that by introducing a small mismatch to the natural frequencies of the metronomes, the probability for generating the anti-phase synchronization (APS) state, i.e., the "odd sympathy" described by Huygens, can be clearly increased. By numerical simulations of the system dynamics, we conduct a detailed analysis on the influence of frequency mismatch on APS. It is found that as the frequency mismatch increases from 0, the attracting basin of APS is gradually enlarged and, in the meantime, the basin of in-phase synchronization (IPS) is reduced. However, as the frequency mismatch exceeds some critical value, both the basins of APS and IPS are suddenly disappeared, resulting in the desynchronization states. The impacts of friction coefficient and synchronization precision on APS are also studied, and it is found that with the increases of the friction coefficient and the precision requirement of APS, the critical frequency mismatch for desynchronization will be decreased.Our study indicates that, instead of luck, Huygens might have introduced, deliberately and elaborately, a small frequency mismatch to the pendulums in his experiment for generating the "odd sympathy".

show abstract

Experimental and numerical study on the basin stability of the coupled metronomes

Cited by 9 publications

References 21 publications

Frequency and Phase Characteristics of Candle Flame Oscillation

Frequency and Phase Characteristics of Candle Flame Oscillation

Experimental study on amplitude-frequency characteristic and basin stability of horizontally driven pendulum

Huygens’ synchronization experiment revisited: luck or skill?

Contact Info

Product

Resources

About