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

TL;DR

This paper investigates how the dilution of network connectivities affects cluster synchronization in adaptively coupled oscillator networks, combining numerical and analytical methods to understand robustness and topology effects.

Contribution

It extends the study of synchronization phenomena to complex, randomly diluted networks, applying the master stability approach to adaptive networks.

Findings

Multicluster states show robustness against network dilution.

Adaptive topology influences synchronization stability.

Analytical methods complement numerical simulations.

Abstract

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.