Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/6829
Title: Hopf bifurcation analysis of a system of coupled delayed-differential equations
Authors: Çelik, Canan
Merdan, Hüseyin
Keywords: Hopf bifurcation
Delay differential equation
Time delay
Stability
Periodic solutions
Issue Date: 2013
Publisher: Elsevier Science Inc
Abstract: In this paper, we have considered a system of delay differential equations. The system without delayed arises in the Lengyel-Epstein model. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. Linear stability is investigated and existence of Hopf bifurcation is demonstrated via analyzing the associated characteristic equation. For the Hopf bifurcation analysis, the delay parameter is chosen as a bifurcation parameter. The stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. (1981) [7]. Furthermore, the direction of the bifurcation, the stability and the period of periodic solutions are given. Finally, the theoretical results are supported by some numerical simulations. (C) 2013 Elsevier Inc. All rights reserved.
URI: https://doi.org/10.1016/j.amc.2012.12.063
https://hdl.handle.net/20.500.11851/6829
ISSN: 0096-3003
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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