Self-replicating spots in the Brusselator model and extreme events in the one-dimensional case with delay

Mustapha Tlidi, Yerali Carolina Gandica Lopez, Giorgio Sonnino, Etienne Averlant, Krassimir Panajotov

Résultats de recherche: Contribution à un journal/une revueArticleRevue par des pairs


We consider the paradigmatic Brusselator model for the study of dissipative structures in far from equilibrium systems. In two dimensions, we show the occurrence of a self-replication phenomenon leading to the fragmentation of a single localized spot into four daughter spots. This instability affects the new spots and leads to splitting behavior until the system reaches a hexagonal stationary pattern. This phenomenon occurs in the absence of delay feedback. In addition, we incorporate a time-delayed feedback loop in the Brusselator model. In one dimension, we show that the delay feedback induces extreme events in a chemical reaction diffusion system. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical distribution, which is often considered as a signature of the presence of rogue waves, appears for sufficiently strong feedback intensity. The generality of our analysis suggests that the feedback-induced instability leading to the spontaneous formation of rogue waves in a controllable way is a universal phenomenon.
langue originaleAnglais
Nombre de pages64
Numéro de publication3
Les DOIs
Etat de la publicationPublié - 28 févr. 2016

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