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Self-Replicating Spots in the Brusselator Model and Extreme Events in the One-Dimensional Case with Delay

par Tlidi, Mustapha ;Gandica, Yérali;Sonnino, Giorgio ;Averlant, Etienne ;Panajotov, Krassimir
Référence Entropy, 18, page (64)
Publication Publié, 2016-02-27

Article révisé par les pairs

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Résumé :

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.