Hopf Bifurcation Analysis of a Class of Abstract Delay Differential Equation

The dynamics of a class of abstract delay differential equationsare investigated. We prove that a sequence of Hopf bifurcations occurat the origin equilibrium as the delay increases. By using the theoryof normal form and centre manifold, the direction of Hopf bifurcationsand the stability of the bifurcating periodic solutions is derived. Then,the existence of the global Hopf bifurcation of the system is discussedby applying the global Hopf bifurcation theorem of general functionaldifferential equation.