Partially synchronized states in an ensemble of chemo-mechanical oscillators

Abstract

Partially synchronized (clustered) states are defined as coexisting coherent (synchronized) and incoherent (unsynchronized) domains in an ensemble of interacting oscillators. We report these clustered states in experiments involving an ensemble of sixteen mercury beating heart (MBH) oscillators. These oscillators interact via resistors and are subjected to two different network schemes: 1) All to all and 2) Nonlocal. For the all to all network, the coupling strengths were inhomogeneously distributed, whereas for the nonlocal network scenario, each oscillator was coupled, with an identical coupling strength, with four of its nearest neighbors in either direction. For both of these network schemes, partially synchronized states results into grouping of these oscillators, wherein some oscillators are synchronized and rest are unsynchronized. For all to all network, the partially synchronized states are observed, for the intermediate inhomogeneities, when subjected to the power law and the ‘U’ shape profiles of coupling strengths. Irrespective of the coupling profile chosen, low inhomogeneities in the coupling strengths leaves all the oscillators in a single coherent state whereas for the high inhomogeneities scenarios oscillators are located in the incoherent domain. In comparison, for the nonlocal network partially synchronized states emerge when the coupling constant is appropriately chosen. The experimental results for both these network scenarios have been analyzed using the redox time series (chemical activity) and the time evolution of the normalized areas for the mercury drop (mechanical activity). The existence of partially synchronized states in the experiments was verified using different diagnostic tools such as time series plot, space–time plot and average frequency.