文献类型：期刊文献

中文题名：高维非线性映射系统的不稳定流形计算方法研究

英文题名：Computation method for unstable manifold of hénon map

作者：贾蒙[1]

第一作者：贾蒙

通讯作者：Jia, Meng

机构：[1]新乡学院机电工程学院

第一机构：新乡学院机电工程学院

年份：2017

卷号：36

期号：17

起止页码：262-266

中文期刊名：振动与冲击

外文期刊名：Journal of Vibration and Shock

收录：CSTPCD;;EI(收录号：20174704430966);Scopus(收录号：2-s2.0-85034272528);北大核心:【北大核心2014】；CSCD:【CSCD2017_2018】；

基金：国家自然科学基金(61501391);河南省高等学校重点科技项目(15A510035)

语种：中文

中文关键词：离散动力系统;双曲不动点;不稳定流形;Hénon映射;混沌

外文关键词：discrete dynamic system; hyperbolic fixed point; unstable manifold; Hénon map; chaos;

摘要：提出了一种基于曲率约束条件的计算离散动力系统鞍型不动点一维不稳定流形的新算法,并以Hénon映射为例进行了计算。新算法以增长流形为基本思想,通过曲率约束和距离控制来确定离散点间的距离;提出流形的偏转角度可以通过流形上的已知点来预测,解决了流形上新点的原像位置快速确定的困难。仿真发现:Hénon映射的一维不稳定流形在标准参数下与Hénon映射产生的散点图分布一致,在其它几组参数下,一维不稳定流形的两个分支之间保持着某种程度的对称性,该研究对Hénon映射的进一步研究打下基础。
A new algorithm was presented for computing one dimensional unstable manifold for saddle fixed point of a discrete dynamic system based on the constraint condition of curvature. Hénon map was taken as an example to check the performance of the algorithm. The manifold growing was taken as the basic idea of the new algorithm. Curvature constraint and distance control were used to determine the distance between discrete points. The unstable manifold grew with new point added at each step and the distance between consecutive points was adjusted according to the local curvature. It was proved that the gradient of the manifold at the new point can be predicted with the known points on the manifold and in this way the preimage of the new point can be located immediately. The simulation showed that the one dimensional unstable manifold of Hénon map coincides with the scatter point diagram distribution produced by itself under standard parameters; under the other several groups of parameters,two branches of the unstable manifold are nearly symmetric,and they serve as the borderline of Hénon map iteration sequence. The results laid a foundation for further studying Hénon map.