Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/6828
Title: Hopf bifurcation analysis of a general non-linear differential equation with delay
Authors: Akkocaoğlu, Hande
Merdan, Hüseyin
Çelik, Canan
Keywords: Hopf bifurcation
Delay differential equation
Time delay
Stability
Periodic solutions
Issue Date: 2013
Publisher: Elsevier Science Bv
Abstract: This work represents Hopf bifurcation analysis of a general non-linear differential equation involving time delay. A special form of this equation is the Hutchinson-Wright equation which is a mile stone in the mathematical modeling of population dynamics and mathematical biology. Taking the delay parameter as a bifurcation parameter, Hopf bifurcation analysis is studied by following the theory in the book by Hazzard et al. By analyzing the associated characteristic polynomial, we determine necessary conditions for the linear stability and Hopf bifurcation. In addition to this analysis, the direction of bifurcation, the stability and the period of a periodic solution to this equation are evaluated at a bifurcation value by using the Poincare normal form and the center manifold theorem. Finally, the theoretical results are supported by numerical simulations. (c) 2012 Elsevier B.V. All rights reserved.
URI: https://doi.org/10.1016/j.cam.2012.06.029
https://hdl.handle.net/20.500.11851/6828
ISSN: 0377-0427
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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