Twisted Bifurcations and Stability of Homoclinic Loop With Higher Dimensions

JIN Yin-lai; ZHU De-ming

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(10): 1076-1082

JIN Yin-lai, ZHU De-ming. Twisted Bifurcations and Stability of Homoclinic Loop With Higher Dimensions[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1076-1082.

Citation:

JIN Yin-lai, ZHU De-ming. Twisted Bifurcations and Stability of Homoclinic Loop With Higher Dimensions[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1076-1082.

Citation:

JIN Yin-lai, ZHU De-ming. Twisted Bifurcations and Stability of Homoclinic Loop With Higher Dimensions[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1076-1082.

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Twisted Bifurcations and Stability of Homoclinic Loop With Higher Dimensions

JIN Yin-lai^1,2,
ZHU De-ming²

1.
Department of Mathematics, Linyi Teachers' University, Linyi, Shandong 276005, P. R. China;

Received Date: 2002-06-18
Rev Recd Date: 2004-03-16
Publish Date: 2004-10-15

Abstract

Abstract

By using the linear independent solutions of the linear variational equation along the homoclinic loop as the demanded local coordinates to construct the Poincar map,the bifurcations of twisted homoclinic loop for higher dimensional systems are studied.Under the nonresonant and resonant conditions,the existence,number and existence regions of the 1-homoclinic loop,1-periodic orbit,2-homoclinic loop,2-periodic orbit and 2-fold 2-periodic orbit were obtained.Particularly,the asymptotic repressions of related bifurcation surfaces were also given.Moreover,the stability of homoclinic loop for higher dimensional systems and nontwisted homoclinic loop for planar systems were studied.
- local coordinate,
- Poincar map,
- twisted bifurcation,
- 1-periodic orbit,
- 2-periodic orbit,
- stability

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References(11)

References

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