  Synchronization in networks of oscillatory units is an emergent phenomenon
present in various systems, such as biological, technological, and social
systems. Many real-world systems 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.
Further, we utilize the master stability approach for adaptive networks in
order to highlight the interplay between adaptivity and topology.
