Slow Passage through a Homoclinic Orbit with Subharmonic Resonances
Slow Passage through a Homoclinic Orbit with Subharmonic Resonances
复制标题
缓慢穿过具有次谐波共振的同宿轨道
DOI：
10.1111/1467-9590.00091
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发表时间：
1998
影响因子：
2.7
通讯作者：
R. Haberman
中科院分区：
文献类型：
--
作者：
Jerry D. Brothers;R. Haberman
针对与双阱势相对应的周期性受力和弱阻尼强非线性振荡器，分析了通过同宿轨道的缓慢通过。多相平均在同宿轨道上合并的无限序列的次谐波共振层处失败。使用时移和恒定相位调整来获得强非线性振荡器在经过每个分谐波谐振之后的精确相位。在未受扰动的同宿轨道附近，解决方案是一大串近同宿轨道，其中一个鞍形方法映射到下一个鞍形方法。匹配渐近展开的方法用于将次谐波共振层中的解与未扰动同宿轨道附近的解联系起来。通过这种方式，我们确定了与每口井捕获相对应的吸引力盆地边界的渐近精确分析描述。
The slow passage through a homoclinic orbit is analyzed for a periodically forced and weakly damped strongly nonlinear oscillator corresponding to a double‐well potential. Multiphase averaging fails at an infinite sequence of subharmonic resonance layers that coalesce on the homoclinic orbit. An accurate phase of the strongly nonlinear oscillator after passage through each subharmonic resonance is obtained using a time shift and a constant phase adjustment. Near the unperturbed homoclinic orbit, the solution is a large sequence of nearly homoclinic orbits in which one saddle approach is mapped into the next. The method of matched asymptotic expansions is used to relate the solution in subharmonic resonance layers to the solution near the unperturbed homoclinic orbit. In this way, we determine an asymptotically accurate analytic description for the boundaries of the basins of attraction corresponding to capture into each well.