Exploring the Mercury Beating Heart system: synchronization dynamics and potential applications in the field of nonlinear dynamics

The Mercury Beating Heart (MBH) system, an intriguing chemo-mechanical oscillator, holds significance in experimental nonlinear dynamics. This system features a mercury droplet in an electrolyte, inducing oscillations through electrochemical reactions at their junction. It offers insights into coupled oscillator dynamics, showcasing synchronization behavior such as partial and explosive synchronization. Its simplicity and diverse dynamic behaviours make it an excellent choice for empirical and theoretical study. This article examines the MBH system's innovation and potential applications, emphasizing topics like topological modes, chemo-mechanical synchronization, and collective behaviour. Notable demonstrations include observing Kuramoto transition via global coupling's mean field interactions and explosive synchronization in star network setups. The goal is to present a comprehensive guide for researchers keen on using the MBH system to deepen our understanding of coupled oscillator dynamics. By exploring intricate synchronization phenomena, this article aims to inspire further investigation, advancing our comprehension and guiding future research paths.