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 journalArticlepeer-review


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
Issue number3
Publication statusPublished - 28 Feb 2016


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


Dive into the research topics of 'Self-replicating spots in the Brusselator model and extreme events in the one-dimensional case with delay'. Together they form a unique fingerprint.

Cite this