Self-Replicating Spots in the Brusselator Model and Extreme Events in the One-Dimensional Case with Delay
AbstractWe 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
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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.
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(3):64.Chicago/Turabian Style
Tlidi, Mustapha; Gandica, Yerali; Sonnino, Giorgio; Averlant, Etienne; Panajotov, Krassimir. 2016. "Self-Replicating Spots in the Brusselator Model and Extreme Events in the One-Dimensional Case with Delay." Entropy 18, no. 3: 64.
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