Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

Synchronization of distributed power grids with the external loading system

In this paper, the synchronization between spatially distributed power plants and their supported consumers is studied, where the case of Kuramoto-like model power grids connected to an external permanent magnet synchronous motor (PMSM) is taken as an example. We focus on the dependence of the synchronization on the coupling coefficient. To quantitatively study the synchronization degree, we introduce the order parameter and the frequency deviation to measure the synchronization of the coupled system. It is found that as the external coupling coefficient is increased, the distributed power grids and the loading system become more and more synchronized in space, and the complete synchronization appears at a particular value of external coupling coefficient. Our results may provide a useful tip for analyzing the synchronous ability of distributed power grids.