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.

Benjamin-“Feir instabilities on directed networks / Di Patti, Francesca; Fanelli, Duccio; Miele, Filippo; Carletti, Timoteo. - In: CHAOS, SOLITONS AND FRACTALS. - ISSN 0960-0779. - STAMPA. - 96:(2017), pp. 8-16. [10.1016/j.chaos.2016.11.018]

Benjamin-“Feir instabilities on directed networks

Di Patti, Francesca
;
Fanelli, Duccio
;
Carletti, Timoteo
2017

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.
2017
96
8
16
Di Patti, Francesca; Fanelli, Duccio; Miele, Filippo; Carletti, Timoteo
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1113188
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