Applications of the Signs of Melnikov’s Function

Shen Jia-qi

Volume 13 Issue 10

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Abstract

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Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(10): 907-910

Shen Jia-qi. Applications of the Signs of Melnikov’s Function[J]. Applied Mathematics and Mechanics, 1992, 13(10): 907-910.

Citation:

Shen Jia-qi. Applications of the Signs of Melnikov’s Function[J]. Applied Mathematics and Mechanics, 1992, 13(10): 907-910.

Citation:

Shen Jia-qi. Applications of the Signs of Melnikov’s Function[J]. Applied Mathematics and Mechanics, 1992, 13(10): 907-910.

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Applications of the Signs of Melnikov’s Function

Shen Jia-qi

Shanghai Normal University, Shanghai

Received Date: 1991-10-25
Publish Date: 1992-10-15

Abstract

Abstract

The existence and stability ol periodic solutions for the two-dimensional system x'=f(x)+εg(x,a),0<ε<<1,a∈R whose unperturbed systemis 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 doublezero eigenvalues.
- Melnikov's function,
- codimension two bifurcations of flows,
- bifurcation set

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References(3)

References

[1]	Carr,J.,Applications of Center Manifold Theory,Springer-Verlag,New York (1981).
[2]	Draohman,B.,S.A.Van Gill and Zhang Zhi-fen,Abelian integrals for quadratic vector field,J.Reine Angew.math.,382(1987),165-180.
[3]	Gukenheimer,J.and P.Holmes.Nonlinear Oscillations,Dynamical Systems,and Bifurcations of Vector Field,Springer-Verlag,New York(1983).

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