Benjamin–Feir instabilities on directed networks

Francesca Di Patti, Duccio Fanelli, Filippo Miele, Timoteo Carletti

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Abstract

The Complex Ginzburg–Landau equation is studied assuming a directed network of coupled oscillators. The asymmetry makes the spectrum of the Laplacian operator complex, and it is ultimately responsible for the onset of a generalized class of topological instability, reminiscent of the Benjamin–Feir type. The analysis is initially carried out for a specific class of networks, characterized by a circulant adjacency matrix. This allows us to delineate analytically the domain in the parameter space for which the generalized instability occurs. We then move forward to considering the family of non linear oscillators coupled via a generic direct, though balanced, graph. The characteristics of the emerging patterns are discussed within a self-consistent theoretical framework.
Original languageEnglish
Pages (from-to)8-16
JournalChaos, Solitons & Fractals
Volume90
DOIs
Publication statusPublished - 1 Mar 2017

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Directed Network
Circulant Matrix
Complex Ginzburg-Landau Equation
Nonlinear Oscillator
Coupled Oscillators
Adjacency Matrix
Asymmetry
Parameter Space
Graph in graph theory
Class
Family
Framework

Keywords

  • Pattern formation
  • reaction-diffusion
  • Coupled oscillators
  • Benjamin-Feir
  • Complex networks

Cite this

Di Patti, Francesca ; Fanelli, Duccio ; Miele, Filippo ; Carletti, Timoteo. / Benjamin–Feir instabilities on directed networks. In: Chaos, Solitons & Fractals. 2017 ; Vol. 90. pp. 8-16.
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Benjamin–Feir instabilities on directed networks. / Di Patti, Francesca ; Fanelli, Duccio; Miele, Filippo; Carletti, Timoteo.

In: Chaos, Solitons & Fractals, Vol. 90, 01.03.2017, p. 8-16.

Research output: Contribution to journalArticle

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