Solitary states in complex networks: impact of topology

TL;DR

This paper explores how network topology influences the emergence of solitary states, where individual nodes behave differently from the rest, especially in asymmetric, scale-free networks, through simulations and bifurcation analysis.

Contribution

It identifies structural network features that promote solitary states and demonstrates their occurrence in asymmetric, scale-free networks using numerical and bifurcation analyses.

Findings

Solitary states are more likely in asymmetric, scale-free networks.

Minimum connections of neighboring nodes are crucial for solitary state emergence.

Bifurcation analysis confirms the role of local connectivity in solitary states.

Abstract

The dynamical behavior of networked systems is expected to reflect the features of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example is provided by the so-called solitary states where the dynamics of one network node is different from the entire symmetric network. Here, we investigate the structural constraints of networks for the appearance of solitary states in their dynamics. By performing a large number of numerical simulations, we find that such states occur with high probability in asymmetric networks, such as the ones exhibiting the scale-free property. Next, we analyze the structural features of the networks demonstrating solitary states to reveal that the minimum number of connections in the adjacent nodes of a solitary one is crucial for the appearance of the solitary states. Finally, we perform bifurcation analysis of a dimension-reduced system, confirming the influence of the connectivity of the neighboring nodes on the solitary ones.