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

Mustapha Tlidi, Yerali Gandica, Giorgio Sonnino, Etienne Averlant, Krassimir Panayotov

Research output: Contribution to journalArticle

13 Citations (Scopus)


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.
Original languageEnglish
Article number64
Pages (from-to)1-10
Number of pages10
Issue number3
Publication statusPublished - Mar 2016


  • localized structures
  • rogue waves
  • extreme events
  • spot self-replication

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