PERIODICALLY PERTURBED HOPF-BIFURCATION

In this paper the influence of small periodic perturbations on systems exhibiting Hopf bifurcation is studied in detail. In two-dimensional systems that ordinarily exhibit Hopf bifurcation, the addition of small periodic parametric excitation gives rise to interesting 'secondary phenomena. ' Explicit results for various primary and secondary bifurcations, along with their stabilities, are obtained. In this work, the ideas related to method of averaging, Poincare-Birkhoff normal forms, and center manifold theorem are used appropriately at different stages. It is found that various results obtained using these techniques agree in their common regions of validity.