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 - <p style="text-align: justify;">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.</p>