Consistency of heterogeneous synchronization patterns in complex weighted networks

Abstract

Synchronization within the dynamical nodes of a complex network is usually considered homogeneous through all the nodes. Here we show, in contrast, that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or asymmetries in small networks. We also analyze consistency, defined as the persistence of coexistent synchronization patterns regardless of the initial conditions. Our results show that complex weighted networks display richer consistency than regular networks, suggesting why certain functional network topologies are often constructed when experimental data are analyzed. Dynamical systems may synchronize in several ways, at the same time, when they are coupled in a single complex network. Examples of this diversity of synchronization patterns may be found in research fields as diverse as neuroscience, climate networks, or ecosystems. Here we report the conditions required to obtain coexisting synchronizations in arrangements of interacting chaotic oscillators, and relate these conditions to the distribution of coupling weights and asymmetries in complex networks. We also analyze the conditions required for a high statistical occurrence of the same synchronization patterns, regardless of the oscillators' initial conditions. Our results show that these persistent synchronization patterns are statistically more frequent in complex weighted networks than in regular ones, explaining why certain functional network topologies are often retrieved from experimental data. Besides, our results suggest that considering both the different coexisting synchronizations and also their statistics may result in a richer understanding of the relations between functional and structural networks of oscillators.

Next Generation Networks: Featuring the Potential Role of Emerging Applications in Translational Oncology

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Principles and open questions in functional brain network reconstruction

“…While it has theoretically been shown that some connectivity patterns are more stable, and hence appear more frequently in any analysis (Malagarriga et al, 2017), the previous studies also highlight that the topological metrics of the reconstructed networks strongly depend on the methodological choices made by the researcher. This is clearly a problem, as it undermines the generalizability of results; but also represents an advantage.…”

Brain synchronizability, a false friend

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