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Benjamin–Feir instabilities on directed networks

Author

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

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.

Suggested Citation

  • Di Patti, Francesca & Fanelli, Duccio & Miele, Filippo & Carletti, Timoteo, 2017. "Benjamin–Feir instabilities on directed networks," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 8-16.
    • Handle: RePEc:eee:chsofr:v:96:y:2017:i:c:p:8-16
    DOI: 10.1016/j.chaos.2016.11.018
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    References listed on IDEAS

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    1. Malbor Asllani & Joseph D. Challenger & Francesco Saverio Pavone & Leonardo Sacconi & Duccio Fanelli, 2014. "The theory of pattern formation on directed networks," Nature Communications, Nature, vol. 5(1), pages 1-9, December.
    2. Duccio Fanelli & Claudia Cianci & Francesca Patti, 2013. "Turing instabilities in reaction-diffusion systems with cross diffusion," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-8, April.
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