高维同宿环扭曲分支与稳定性

基金项目: 国家自然科学基金资助项目(10371040)

Twisted Bifurcations and Stability of Homoclinic Loop With Higher Dimensions

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

摘要: 利用沿同宿环的线性变分方程的线性独立解作为在同宿环的小管状邻域内的局部坐标系来建立Poincaré映射，研究了高维系统扭曲同宿环的分支问题．在非共振条件和共振条件下，获得了1-同宿环、 1-周期轨道、 2-同宿环、 2-周期轨道和两重2-同期轨道的存在性、存在个数和存在区域．给出了相关的分支曲面的近似表示．同时，研究了高维系统同宿环和平面系统非扭曲同宿环的稳定性．
- 局部坐标 /
- Poincaré映射 /
- 扭曲分支 /
- 1-周期轨 /
- 2-周期轨 /
- 稳定性
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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