Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/1670
Title: An algorithm for Hopf bifurcation analysis of a delayed reaction-diffusion model
Authors: Kayan, S.
Merdan, Hüseyin
125872
Keywords: Hopf bifurcation
Delay differential equations
Reaction-diffusion equation
Stability
Time delay
Periodic solutions
Issue Date: Jul-2017
Publisher: Springer
Source: Kayan, Ş., & Merdan, H. (2017). An algorithm for Hopf bifurcation analysis of a delayed reaction–diffusion model. Nonlinear Dynamics, 89(1), 345-366.
Abstract: We present an algorithm for determining the existence of a Hopf bifurcation of a system of delayed reaction-diffusion equations with the Neumann boundary conditions. The conditions on parameters of the system that a Hopf bifurcation occurs as the delay parameter passes through a critical value are determined. These conditions depend on the coefficients of the characteristic equation corresponding to linearization of the system. Furthermore, an algorithm to obtain the formulas for determining the direction of the Hopf bifurcation, the stability, and period of the periodic solution is given by using the Poincare normal form and the center manifold theorem. Finally, we give several examples and some numerical simulations to show the effectiveness of the algorithm proposed.
URI: https://doi.org/10.1007/s11071-017-3458-5
https://hdl.handle.net/20.500.11851/1670
ISSN: 0924-090X
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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