Hubs-attracting laplacian and related synchronization on networks

Gambuzza, Lucía V. ; Frasca, Mattia ; Estrada, Ernesto

Resumen: In this work, we introduce a new Laplacian matrix, referred to as the hubs-attracting Laplacian, accounting for diffusion processes on networks where the hopping of a particle occurs with higher probability from low to high degree nodes. This notion complements the one of the hubs-repelling Laplacian discussed in [E. Estrada, Linear Algebra Appl., 596 (2020), pp. 256-280], that considers the opposite scenario, with higher hopping probabilities from high to low degree nodes. We formulate a model of oscillators coupled through the new Laplacian and study the synchronizability of the network through the analysis of the spectrum of the Laplacian. We discuss analytical results providing bounds for the quantities of interest for synchronization and computational results showing that the hubs-attracting Laplacian generally has better synchronizability properties when compared to the classical one, with a low occurrence rate for the graphs where this is not true. Finally, two illustrative case studies of synchronization through the hubs-attracting Laplacian are considered.

Idioma: Inglés

DOI: 10.1137/19M1287663

Año: 2020

Publicado en: SIAM Journal on Applied Dynamical Systems 19, 2 (2020), 1057-1079
ISSN: 1536-0040

Factor impacto JCR: 2.316 (2020)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 12 / 55 = 0.218 (2020) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 53 / 265 = 0.2 (2020) - Q1 - T1

Factor impacto SCIMAGO: 1.218 - Modeling and Simulation (Q1) - Analysis (Q1)

Tipo y forma: Article (Published version)