Huygens’ synchronization experiment revisited: luck or skill?

Abstract

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".

Forward Entrainment: Evidence, Controversies, Constraints, and Mechanisms

“…Interestingly, in a letter to his father Huygens notes that while confined at home with a brief illness, he observed that paired clocks always swung 180 degrees out of phase when synchronized. More recent experiments have demonstrated that a small oscillation frequency difference between the two clocks enhances antiphasic synchronization (Czolczynski et al, 2010;Willms, 2017;Yang et al, 2018). The resultant oscillation frequency of the coupled system is between the oscillation frequencies of the two clocks and does not match one or the other as is the case with neural or psychophysical studies of entrainment using an external driving modulator that directionally captures the behavior of the entrained system.…”

Forward entrainment: Psychophysics, neural correlates, and function

“…Interestingly, in a letter to his father Huygens notes that while confined at home with a brief illness, he observed that paired clocks always swung 180° degrees out of phase when synchronized. More recent experiments have demonstrated that a small oscillation frequency difference between the two clocks enhances antiphasic synchronization (Czolczynski et al, 2010(Czolczynski et al, , 2011Willms, 2017;Yang et al, 2018). The resultant oscillation frequency of the coupled system is between the oscillation frequencies of the two clocks and does not match one or the other, in contrast to the case of neural or psychophysical studies of entrainment using an external driving modulator that directionally captures the behavior of the entrained system.…”

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

“…In a letter to his father, Huygens referred to this odd phenomenon as 'the sympathy of two clocks' [2]. Nowadays, this sympathy is known as Huygens' synchronization [3][4][5] and the suspended bar coupling the clocks is referred to as Huygens' coupling [6,7].…”