Nonresonant periodic perturbation of the hopf bifurcation

In this paper the following periodically perturbed autonomous system text omatted in which g is 2π/ω-periodic in t and f(0,η) = 0 is considered. It is assumed that the autonomous system obtained by setting b=0 undergoes a generic Hopf bifurcation from x = 0 at η= 0 and that the frequency,ω, is not in resonance with the frequency of the Hopf periodic solution. Under these conditions, we show that an integral manifold of solutions bifurcates from the unique 2π/ω-periodic solution, x*, of (1) on one side of the neutral stability curve for x* in the (b,η) plane.