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Solitary states in complex networks: impact of topology

Schülen, Leonhard; Mikhailenko, Maria; Medeiros, Everton S.; Zakharova , Anna

The dynamical behavior of networked systems is expected to reflect the properties of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example are so-called solitary states where the dynamics of one network node is different from the synchronized rest. Here, we investigate the structural constraints of networks for the appearance of solitary states. By performing a large number of numerical simulations, we find that such states occur with high probability in asymmetric networks, among them scale-free ones. We analyze the structural properties of the networks that support solitary states. We demonstrate that the minimum neighbor node degree of a solitary node is crucial for the appearance of solitary states. Finally, we perform bifurcation analysis of dimension-reduced systems, which confirm the importance of the connectivity of the neighboring nodes.
Published in: European physical journal special topics, 10.1140/epjs/s11734-022-00713-4, Springer Nature