Nonresonant periodic perturbation of the hopf bifurcation

Abstract

In this paper the following periodically perturbed autonomous system

in which g is 2π/υ-periodic in t and is considered. It is assumed that tne 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 solutionx∗, of (1) on one side of the neutral stability curve for x∗ in the (b,η) plane.