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Entropy 2016, 18(3), 64;

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

Faculté des Sciences, Université Libre de Bruxelles, Campus Plaine, C.P. 231, Brussels B-1050, Belgium
Namur Center for Complex Systems (naXys), University of Namur, Rempart de la Vierge 8, Namur B-5000, Belgium
Department of Applied Physics and Photonics (IR-TONA), Vrije Universiteit Brussel, Pleinlaan 2, Brussels B-1050, Belgium
Institute of Solid State Physics, 72 Tzarigradsko Chaussee Blvd., Sofia 1784, Bulgaria
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 29 November 2015 / Revised: 7 February 2016 / Accepted: 18 February 2016 / Published: 27 February 2016
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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. View Full-Text
Keywords: localized structures; spot self-replication; extreme events; rogue waves localized structures; spot self-replication; extreme events; rogue waves

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Tlidi, M.; Gandica, Y.; Sonnino, G.; Averlant, E.; Panajotov, K. Self-Replicating Spots in the Brusselator Model and Extreme Events in the One-Dimensional Case with Delay. Entropy 2016, 18, 64.

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