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

Research output: Contribution to journalArticle

Abstract

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
Number of pages64
JournalEntropy
Volume18
Issue number3
DOIs
Publication statusPublished - 28 Feb 2016

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pulse amplitude
statistical distributions
chemical reactions
fragmentation
signatures
occurrences

Keywords

  • Extreme events
  • Localized structures
  • Rogue waves
  • Spot self-replication

Cite this

Tlidi, Mustapha ; Gandica Lopez, Yerali Carolina ; Sonnino, Giorgio ; Averlant, Etienne ; Panajotov , Krassimir . / Self-replicating spots in the Brusselator model and extreme events in the one-dimensional case with delay. In: Entropy. 2016 ; Vol. 18, No. 3.
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Self-replicating spots in the Brusselator model and extreme events in the one-dimensional case with delay. / Tlidi, Mustapha; Gandica Lopez, Yerali Carolina; Sonnino, Giorgio; Averlant, Etienne; Panajotov , Krassimir .

In: Entropy, Vol. 18, No. 3, 28.02.2016.

Research output: Contribution to journalArticle

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