Effect of diluted connectivities on cluster synchronization of adaptively coupled oscillator networks

Abstract

Synchronization in networks of oscillatory units is an emergent phenomenon that has been observed in various systems, from power grids to ensembles of nerve cells. Many real-world networks have adaptive properties, meaning that their connectivities change with time, depending on the dynamical state of the system. Networks of adaptively coupled oscillators show various synchronization phenomena, such as hierarchical multifrequency clusters, traveling waves, or chimera states. While these self-organized patterns have been previously studied on all-to-all coupled networks, this work extends the investigations towards more complex networks, analyzing the influence of random network topologies for various degrees of dilution of the connectivities. Using numerical and analytical approaches, we investigate the robustness of multicluster states on networks of adaptively coupled Kuramoto-Sakaguchi oscillators against the random dilution of the underlying network topology. We utilize the master stability approach for adaptive networks in order to highlight the interplay between adaptivity and topology. With this, we show the robustness of multifrequency cluster states to diluted connectivities.