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Title: Hopf Bifurcations Of A Lengyel-Epstein Model Involving Two Discrete Time Delays
Authors: Bilazeroğlu, Şeyma
Merdan, Hüseyin
Guerrini, Luca
Keywords: Lengyel-Epstein system
oscillating reaction
Hopf bifurcation
delay differential equation
functional differential equation
time delay
periodic solutions
Diffusion-Driven Instability
Turing Patterns
Issue Date: 2021
Publisher: Amer Inst Mathematical Sciences-Aims
Abstract: Hopf bifurcations of a Lengyel-Epstein model involving two discrete time delays are investigated. First, stability analysis of the model is given, and then the conditions on parameters at which the system has a Hopf bifurcation are determined. Second, bifurcation analysis is given by taking one of delay parameters as a bifurcation parameter while fixing the other in its stability interval to show the existence of Hopf bifurcations. The normal form theory and the center manifold reduction for functional differential equations have been utilized to determine some properties of the Hopf bifurcation including the direction and stability of bifurcating periodic solution. Finally, numerical simulations are performed to support theoretical results. Analytical results together with numerics present that time delay has a crucial role on the dynamical behavior of Chlorine Dioxide-Iodine-Malonic Acid (CIMA) reaction governed by a system of nonlinear differential equations. Delay causes oscillations in the reaction system. These results are compatible with those observed experimentally.
ISSN: 1078-0947
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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