What is it about?

This article deals with two of the most fascinating and ubiquitous natural phenomena: synchronization and resonance. The starting point is a precise and assigned network structure. The goal is to study such phenomena when the framework of connections between network elements is predetermined. Such elements are modeled as identical harmonic oscillators. What frequencies make a network of interacting subjects resonate? Which nodes drag the network along and which are transparent to the oscillating frequencies? These are some of the questions the article seeks to answer. The theoretical results are then applied to a specific social network and power grid.

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Why is it important?

The results proposed in the paper provide an in-depth understanding of some of the most interesting natural and social cooperative processes. For instance, they allow to catch the effectiveness of a driving force applied on a specific node of the network.


Interesting extensions for future works may be the following: (a) a study of the effect of symmetries in the topological structure of the network and a comparison between the response of the full network and of the so-called quotient network under network automorphisms, (b) the analysis of the effect of topologies described by non-normal matrices on the transient dynamics and the relationship between the degree of non-normality and the resilience properties of the networked dynamical system, or, finally, (c) the introduction of non-local interactions through generalizations of the Laplacian and of an external stress factor acting on the network in order to assess their impact on resonance and synchronization outcomes.

Paolo Bartesaghi
Universita degli Studi di Milano-Bicocca

Read the Original

This page is a summary of: Notes on resonant and synchronized states in complex networks, Chaos An Interdisciplinary Journal of Nonlinear Science, March 2023, American Institute of Physics,
DOI: 10.1063/5.0134285.
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