Structural and functional networks in complex systems with delay

Abstract

Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes), and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology, b, is related to the exponent of the associated functional network as a =1/(2-b), for b < 2.

5 pages, 3 figures

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• Estimating the impact of structural directionality: How reliable are undirected connectomes?
• Role of delay in the mechanism of cluster formation
• Synchronization Invariance Under Network Structural Transformations
• The effect of distributed time-delays on the synchronization of neuronal networks
• Delay-induced driven patterns in coupled Cayley tree networks