Year: 2022
Author: Fengyuan Zhong, Zicheng Xu, Bin Ge
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 2 : pp. 277–290
Abstract
The dynamics of a class of abstract delay differential equations are investigated. We prove that a sequence of Hopf bifurcations occur at the origin equilibrium as the delay increases. By using the theory of normal form and centre manifold, the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions is derived. Then, the existence of the global Hopf bifurcation of the system is discussed by applying the global Hopf bifurcation theorem of general functional differential equation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2022.277
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 2 : pp. 277–290
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Hopf bifurcation Delay Stability Normal form Periodic solution.