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Article

On the complex Ginzburg-Landau equation with a delayed feedback

Publicated to:Mathematical Models & Methods In Applied Sciences. 16 (1): 1-17 - 2006-01-01 16(1), DOI: 10.1142/S0218202506001030

Authors: Casal, AC; Diaz, JI;

Affiliations

Univ Complutense Madrid, Fac Math, Dept Matemat Aplicada, E-28040 Madrid, Spain - Author
UNIV POLITECN MADRID, ETS ARQUITECTURA, DEPT MATEMAT APLICADA, E-28040 MADRID, SPAIN - Author

Abstract

We show how to stabilize the uniform oscillations of the complex Ginzburg-Landau equation with periodic boundary conditions by means of some global delayed feedback. The proof is based on an abstract pseudo-linearization principle and a careful study of the spectrum of the linearized operator.

Keywords

Complex ginzburg-landau equationLinearized stabilityNon-local delayed controlPrinciple of pseudo-linearized stabilityTurbulence

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Mathematical Models & Methods In Applied Sciences due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2006, it was in position 7/150, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 5.8, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-13, the following number of citations:

  • WoS: 10
  • Scopus: 10
  • OpenCitations: 13

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-13:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 1 (PlumX).

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (CASAL PIGA, ALFONSO CARLOS) .

the author responsible for correspondence tasks has been CASAL PIGA, ALFONSO CARLOS.