Hopf Bifurcation Analysis of a Class of Abstract Delay Differential Equation

Hopf Bifurcation Analysis of a Class of Abstract Delay Differential Equation

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.

Author Details

Fengyuan Zhong

Zicheng Xu

Bin Ge