Melnikov's Method and Codimension-Two Bifurcations in Forced Oscillations |
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Authors: | Kazuyuki Yagasaki |
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Affiliation: | Department of Mechanical and Systems Engineering, Gifu University, Gifu, Gifu, 501-1193, Japanf1yagasaki@cc.gifu-u.ac.jpf1 |
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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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Keywords: | Melnikov method subharmonic orbit Bogdanov-Takens bifurcation homoclinic tangency forced oscillator. |
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