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

Synchronization of networks of oscillatory units is an emergent phenomenon that has been observed in a variety of systems from power grids to ensembles of nerve cells. Many real-world networks are characterized by adaptive properties; in other words, depending on the dynamical states of the system, their connectivity changes with time. Networks of adaptively coupled oscillators exhibit different synchronization phenomena such as hierarchical multifrequency clusters, traveling waves, or chimera states. While these self-organized patterns have been previously studied in all-to-all coupled networks, the present study further investigated more complex networks by analyzing the effect of random network topologies with different dilution degrees of connectivity. The numerical and analytical approaches were employed to investigate the robustness of multi-cluster states on networks of adaptively coupled Kuramoto-Sakaguchi oscillators against random dilution of the underlying network topology. In addition, a master stability approach was used in adaptive networks to highlight the interplay between adaptivity and topology. Through this approach, the robustness of multifrequency cluster states to diluted connectivities can be illustrated.