Abstract
The existence and stability of periodic solutions for the two-dimensional system x′=f(x)+ɛg(x,α), 0<ɛ≪1, α∈R whose unperturbed system is Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with double zero eigenvalues.
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References
Carr, J.,Applications of Center Manifold Theory, Springer-Verlag, New York (1981).
Draohman, B., S. A. Van Gill and Zhang Zhi-fen, Abelian integrals for quadratic vector field,J. Reine Angew. math., 382 (1987), 165–180.
Gukenheimer, J. and P. Holmes,Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Field, Springer-Verlag, New York (1983).
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Communicated by Xu Zheng-fan
The project is supported by the National Natural Science Foundation of China.
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Jia-qi, S. Applications of the signs of Melnikov's function. Appl Math Mech 13, 947–950 (1992). https://doi.org/10.1007/BF02453337
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DOI: https://doi.org/10.1007/BF02453337