Melnikov's method and codimension-two bifurcations in forced oscillations

Using a Melnikov-type technique, we study codimension-two bifurcations called the Bogdanov-Takens bifurcations for subharmonics in periodic perturbations of planar Hamiltonian systems. We give a criterion for the occurrence of the Bogdanov-Takens bifurcations and present approximate expressions for saddle-node, Hopf and homoclinic bifurcation sets near the Bogdanov-Takens bifurcation points. We illustrate the theoretical result with an example. (C) 2002 Elsevier Science (USA).