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

[摘要] 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).

[发布日期] 2002-10-10

[关键词] Melnikov method;subharmonic orbit;Bogdanov-Takens bifurcation;homoclinic tangency;forced oscillator