# Generating directed networks with prescribed Laplacian spectra

Sara Nicoletti, Timoteo Carletti, Duccio Fanelli, Giorgio Battistelli, Luigi Chisci

Résultats de recherche: Contribution à un journal/une revueArticleRevue par des pairs

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## Résumé

Complex real-world phenomena are often modeled as dynamical systems on networks. In many cases of interest, the spectrum of the underlying graph Laplacian sets the system stability and ultimately shapes the matter or information flow. This motivates devising suitable strategies, with rigorous mathematical foundation, to generate Laplacians that possess prescribed spectra. In this paper, we show that a weighted Laplacian can be constructed so as to {\it exactly} realize a desired {\it complex} spectrum. The method configures as a non trivial generalization of existing recipes which assume the spectra to be real. Applications of the proposed technique to (i) a network of Stuart-Landau oscillators and (ii) to the Kuramoto model are discussed. Synchronization can be enforced by assuming a properly engineered, signed and weighted, adjacency matrix to rule the pattern of pairing interactions.
langue originale Anglais 015004 18 Journal of Physics: Complexity 2 1 30 sept. 2020 https://doi.org/10.1088/2632-072X/abbd35 Publié - 1 oct. 2020

## Empreinte digitale Examiner les sujets de recherche de « Generating directed networks with prescribed Laplacian spectra ». Ensemble, ils forment une empreinte digitale unique.

• ### Sara Nicoletti

Timoteo Carletti (Hôte)

3 juin 201930 août 2019

Activité: Types d'Accueil d'un visiteurAccueil d'un étudiant/un stagiaire