相关论文: Synchronization of clocks and metronomes:A perturb…

In 1665, Christiaan Huygens reported the observation of the synchronization of two pendulum clocks hanged on the wall of his workshop. After synchronization, the clocks swung exactly in the same frequency and $180^{o}$ out of phase --…

The synchronization of two pendulum clocks hanging from a wall was first observed by Huygens during the XVII century. This type of synchronization is observed in other areas, and is fundamentally different from the problem of two clocks…

We introduce an interaction mechanism between oscillators leading to exact anti-phase and in-phase synchronization. This mechanism is applied to the coupling between two nonlinear oscillators with a limit cycle in phase space, leading to a…

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…

This paper investigates the synchronization of three identical oscillators, or clocks, suspended from a common rigid support. We consider scenarios where each clock interacts with the other two, achieving synchronization through small…

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…

This study examines the synchronization of three identical oscillators arranged in an array and coupled by small impacts, wherein each oscillator interacts solely with its nearest neighbor. The synchronized state, which is asymptotically…

Various oscillatory phenomena occur in the world. Because some oscillations are related to abnormal states (e.g., particular diseases), establishing state-transition methods from an oscillatory to a resting state is important. In this…

We numerically study the synchronization of two nonidentical pendulum motions, pivoting on a common movable frame in the point of view of the dynamic phase transition. When the difference in the pendulum lengths is not too large, it is…

Weakly coupled oscillators adjust their dynamics to work in unison: they synchronize. This ubiquitous phenomenon is observed for oscillating pendulum, electronic devices, as well as clapping crowds or flashing fireflies. In effect,…

Spontaneous synchronization of an ensemble of metronomes placed on a freely rotating platform is studied experimentally and by computer simulations. A striking in-phase synchronization is observed when the metronomes' beat frequencies are…

Coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of complex dynamical systems, as well as a classical setup for classroom demonstrations of synchronization phenomena. Whereas previous studies of…

The model we consider consists in a double pendulum set, where the pivot points are free to shift along a horizontal line. Moreover, the two pendula are coupled by means of a spring whose extremities connect two points of each pendulum, at…

In this paper we present an experimental setup and an associated mathematical model to study the synchronization of two self sustained strongly coupled mechanical oscillators (metronomes). The effects of a small detuning in the internal…

The phenomenon of phase synchronization was evidenced in the 17th century by Huygens while observing two pendulums of clocks leaning against the same wall. This phenomenon has more recently appeared as a widespread phenomenon in nature, and…

We propose a quantum analogue of the Huygens clock, in which the phases of two spins achieve synchronization through their interaction with a shared environment. The environment functions analogously to the escapement mechanism in a…

The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…

This paper investigates the dynamical system governing the phase differences between three identical oscillators arranged symmetrically and coupled by burst interactions. By constructing a discrete Lyapunov function, we prove the existence…

We analyze the dynamics of a driven, damped pendulum as used in mechanical clocks. We derive equations for the amplitude and phase of the oscillation, on time scales longer than the pendulum period. The equations are first order ODEs and…