Solitary states in complex networks: impact of topology

Abstract

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.

A Review of Pattern Recognition and Machine Learning

“…Schülen, Mikhailenko, Medeiros, and Zakharova [20] presented a novel optimization methodology for designing Minimum-Neighbor-Node (MNN) systems, utilizing granular computing rules and a firefly approach. The advantages and effectiveness of the suggested technique are evaluated through the utilization of established ear and face databases for human recognition [22].…”

Collective behavior of nonlinear dynamical oscillators

“…Other collective behaviors such as cluster chimera death, cluster oscillation death, imperfect amplitude chimera, and multi-chimera death state are also observed in this study. In [34], the authors concentrate on the mechanism of the formation of the solitary state in complex networks. This study considers three different network topologies: a symmetric nonlocally coupled ring, a random, and a scale-free network.…”