Open AccessHopf bifurcations of a Lengyel-Epstein model involving two discrete time delays
Author(s) -
Ş. Bilazeroğlu,
H. Merdan,
Luca Guerrini
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021150
Subject(s) - hopf bifurcation , mathematics , center manifold , bifurcation diagram , stability (learning theory) , pitchfork bifurcation , mathematical analysis , biological applications of bifurcation theory , period doubling bifurcation , bifurcation , nonlinear system , delay differential equation , differential equation , physics , computer science , quantum mechanics , machine learning
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.