Volume 4, Issue 2
Hopf Bifurcation Analysis of a Class of Abstract Delay Differential Equation

Fengyuan Zhong, Zicheng Xu & Bin Ge

J. Nonl. Mod. Anal., 4 (2022), pp. 277-290.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • AMS Subject Headings

34K18, 92D25

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COPYRIGHT: © Global Science Press

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@Article{JNMA-4-277, author = {Zhong , FengyuanXu , Zicheng and Ge , Bin}, title = {Hopf Bifurcation Analysis of a Class of Abstract Delay Differential Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {2}, pages = {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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.277}, url = {http://global-sci.org/intro/article_detail/jnma/20707.html} }
TY - JOUR T1 - Hopf Bifurcation Analysis of a Class of Abstract Delay Differential Equation AU - Zhong , Fengyuan AU - Xu , Zicheng AU - Ge , Bin JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 277 EP - 290 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.277 UR - https://global-sci.org/intro/article_detail/jnma/20707.html KW - Hopf bifurcation, Delay, Stability, Normal form, Periodic solution. AB -

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.

Zhong , FengyuanXu , Zicheng and Ge , Bin. (2022). Hopf Bifurcation Analysis of a Class of Abstract Delay Differential Equation. Journal of Nonlinear Modeling and Analysis. 4 (2). 277-290. doi:10.12150/jnma.2022.277
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