Hopf Bifurcation Analysis of a Class of Abstract Delay Differential Equation (Journal of Nonlinear Modeling and Analysis, 2024)
The dynamics of a class of abstract delay differential equationsare investigated. We prove that a sequence of Hopf bifurcations occur at theorigin equilibrium as the delay increases. By using the theory of normal formand centre manifold, the direction of Hopf bifurcations and the stability of thebifurcating periodic solutions is derived. Then, the existence of the global Hopfbifurcation of the system is discussed by applying the global Hopf bifurcationtheorem of general functional differential equation.