Abstract
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.
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