Kuramoto transition in an ensemble of mercury beating heart systems

We have studied, experimentally, the collective behavior of the electrically coupled autonomous Mercury Beating Heart (MBH) systems exhibiting the breathing mode, by varying both the coupling strength and the population size (from N = 3 to N = 16). For a fixed N, the electrical and the mechanical activities of the MBH systems achieve complete synchronization at different coupling strengths. The electrical activity of each MBH system is measured by the corresponding electrode potential (Ei = Vi). Additionally, the mechanical activity of each MBH oscillator is visually observed (snapshots and video clips). Subsequently, this activity is quantified by calculating the temporal variation in the area (Ai) of the Hg drop. As a result, the synchronization of the electrical (Ei = Vi) and the mechanical (Ai) activities can be measured. The extent of synchronization was quantified by employing the order parameter (r). Our experimental results are found to be in agreement with the Kuramoto theory.