Complexity and heterogeneity in a dynamic network. (March 2018)

• Record Type: Journal Article
• Authors: Lambert, David; Vanni, Fabio
• Is Part Of: Chaos, solitons and fractals. Volume 108(2018)
• Page Start: 94
• Page End: 103
• Publication Date: 2018-03
• Subjects: Complexity -- Phase transition -- Network formation -- Network value -- Stochastic process -- Critical phenomena -- Long-range correlations; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2018.01.024
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: We present an approximate analytical solution for the connectivity of a network model with a "non-simultaneous" linking scheme. This model exhibits node-space correlations in the link distribution, anomalous fluctuations in the time series of the connectivity variable, and a finite-size effect: the maximum number of links occurs away from the critical value of the system parameter. We derive an exact Master Equation for this model in the form of an infinitesimal time-evolution operator. Fluctuations are much more important than the mean-field approximation predicts, which we attribute to the heterogeneity in the model. Finally, we give a sketch of possible real world applications where the value of a network is related to the number of links.