Spectral control for ecological stability

Cencetti, Giulia; Bagnoli, Franco; Battistelli, Giorgio; Chisci, Luigi; Fanelli, Duccio

doi:10.1140/epjb/e2018-90059-y

Cited by 2 publications

(1 citation statement)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similarly, synchronization, a widespread phenomenon in distributed systems, can be enforced by properly adjusting the spectrum of the matrix which encodes for intertwined pairings. Based on the above, it is therefore essential to devise suitably tailored recipes for generating networks, which display a prescribed Laplacian spectrum, compatible with the stability constraint [13,14].…”

Section: Introductionmentioning

confidence: 99%

Generating directed networks with prescribed Laplacian spectra

Nicoletti¹,

Carletti²,

Fanelli³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

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 Laplacian that possess prescribed spectra. In this paper, we show that a weighted Laplacians can be constructed so as to exactly realize a desired 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.

show abstract

Section: Introductionmentioning

confidence: 99%

Generating directed networks with prescribed Laplacian spectra

Nicoletti¹,

Carletti²,

Fanelli³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Generating directed networks with prescribed Laplacian spectra

Nicoletti¹,

Carletti²,

Fanelli³

et al. 2020

J. Phys. Complex.

View full text Add to dashboard Cite

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 exactly realize a desired 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.

show abstract

Spectral control for ecological stability

Cited by 2 publications

References 27 publications

Generating directed networks with prescribed Laplacian spectra

Generating directed networks with prescribed Laplacian spectra

Generating directed networks with prescribed Laplacian spectra

Contact Info

Product

Resources

About