%0 Journal Article
%T Estimation of Shadowing Trajectory of the Nonlinear Systemfrom a Noisy Scalar Series<br>由单变量受扰观测序列估计非线性系统重影轨迹
%A Zhang Zheng-wei
%A Fan Yang-yu
%A Wang Jie-tai
%A <br>张政伟
%A 樊养余
%A 王结太
%J 电子与信息学报
%D 2008
%I 
%X The presence of homoclinic tangencies and homoclinic intersection makes it very difficult, sometimes even impossible, to estimate the shadowing trajectory of the non-hyperbolic nonlinear system. A new algorithm for shadowing the non-hyperbolic nonlinear system is presented in this paper, which is geometrical in nature and tries to exploit the properties of the chaotic systems. Different from former methods, this method computes the stable and unstable manifolds of the noisy trajectory firstly, and then the locations of the homoclinic tangencies are determined. Thus the effects of the homoclinic tangencies on the algorithm can be decreased to a great extent, and the length of the shadowing trajectories are estimated by the locations of these homoclinic tangencies. Also different from those methods which take it as granted that the mechanism of failure of shadowing algorithms is related with the homoclinic tangencies only, experiments in this paper demonstrate a quantitative relation between the minimal distance of homoclinic intersections and the amplitude of noise. Thus the probability that the algorithm converges to the true trajectory can be boosted efficiently, and without any doubts, this strategy can be as a heuristic approach to other methods.
%K Non-hyperbolic nonlinear system
%K Shadowing trajectory
%K Local stable manifolds
%K Homoclinic tangencies Homoclinic intersection<br>非双曲线型非线性系统
%K 轨迹重影
%K 局部稳定流
%K 同宿切面
%K 同宿截面
%K 单变量
%K 受扰
%K 观测
%K 序列估计
%K 非线性系统
%K 轨迹
%K Series
%K Scalar
%K Nonlinear
%K Trajectory
%K 有益的启示
%K 定量
%K 关系
%K 声幅
%K 干扰
%K 最小距离
%K 研究
%K 性能影响
%K 文献
%K 长度
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=1319827C0C74AAE8D654BEA21B7F54D3&jid=EFC0377B03BD8D0EF4BBB548AC5F739A&aid=DD7CCA2F7AD5AB64844AF217B1B84EC9&yid=67289AFF6305E306&vid=340AC2BF8E7AB4FD&iid=0B39A22176CE99FB&sid=23410D0BDB501DF5&eid=5F8BAECF36EB55E2&journal_id=1009-5896&journal_name=电子与信息学报&referenced_num=0&reference_num=14