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Existence of Impact Period-1 Orbit After Grazing Bifurcation for a Soft Impacting System
International Journal of Bifurcation and Chaos ( IF 2.2 ) Pub Date : 2021-06-18 , DOI: 10.1142/s0218127421501030
Shihui Fu 1
Affiliation  

In the paper, the theoretical study on some experimental and numerical results of grazing bifurcation for a soft impacting system are analyzed. After the conditions under which nonimpact period-1 orbit and grazing bifurcation exist are given, we prove that an impact period-1 orbit exists by the implicit function theorem. The details of these periodic orbits are also investigated, which also helps us numerically find them. The method in this paper is still efficient for the multiperiodic orbits with single impact.

中文翻译:

软撞击系统掠分岔后撞击周期一轨道的存在

本文对软冲击系统掠射分岔的一些实验和数值结果的理论研究进行了分析。在给出了非冲击一期轨道和掠分岔存在的条件后,我们利用隐函数定理证明了冲击一期轨道的存在。还研究了这些周期性轨道的细节,这也有助于我们在数值上找到它们。本文的方法对于单次撞击的多周期轨道仍然有效。
更新日期:2021-06-18
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