Stationary localized structures and the effect of the delayed feedback in the brusselator model

B. Kostet, M. Tlidi, F. Tabbert, T. Frohoff-Hülsmann, S. V. Gurevich, E. Averlant, R. Rojas, G. Sonnino, K. Panajotov

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

6 Citas (Scopus)


The Brusselator reaction–diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the Brusselator model. By using numerical continuation methods in two spatial dimensions, we establish a bifurcation diagram showing the emergence of localized spots. We characterize the transition from a single spot to an extended pattern in the form of squares. In the second part, we incorporate delayed feedback control and show that delayed feedback can induce a spontaneous motion of both localized and periodic dissipative structures. We characterize this motion by estimating the threshold and the velocity of the moving dissipative structures. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

Idioma originalInglés
Número de artículo20170385
PublicaciónPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
EstadoPublicada - 28 dic. 2018
Publicado de forma externa


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