Synchronization occurs widely in natural and technological world, but it has not been widely used to extend the life time of the desirable behavior of the coupled systems. Here we consider the globally coupled system consisting of n units and show that the initial synchronous state extends the lifetime of desired behavior of the coupled system in the case when the excitation of one or few units is suddenly (breakdown of energy supply) or gradually (as the effect of aging and fatigue) switched off. We give evidence that for the properly chosen coupling the energy transfer from the excited units allows unexcited units to operate in the desired manner. As proof of concept, we examine the system of coupled externally excited rotating pendula. After the partial excitation switch off the initial complete synchronization of all pendula is replaced by phase synchronization with a constant phase shift between the clusters of excited and unexcited pendula. Our results show that the described extension of the system's life time occurs for the wide range of coupling parameters and is robust to the external perturbations.
We study the synchronization of two rotating pendula mounted on a horizontal beam, which can roll on the parallel surface. The pendula are forced to rotate by different driving torques. It has been shown that after a transient two different types of synchronization between the pendula can be observed. The approximate analytical methods allow us to derive the synchronization conditions and explain the observed types of synchronous configurations. The energy balance in the system allows us to show how the energy is transferred between the pendula via the oscillating beam.
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