Detecting unstable periodic orbits of chaotic dynamical systems

被引:123
作者
Schmelcher, P
Diakonos, FK
机构
[1] Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Heidelberg, 69120
关键词
D O I
10.1103/PhysRevLett.78.4733
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A method to detect the unstable periodic orbits of a chaotic dynamical system is developed. For a given dynamical system our approach allows us to locate the unstable periodic cycles of, in principle, arbitrary length with a high accuracy. Preknowledge of the dynamical system is not required. To demonstrate its reliability as well as efficiency we apply it to several two-dimensional chaotic maps. In the case of short chaotic time series we develop a dynamical algorithm which is based on a mean-field approach via the Voronoi diagram belonging to the time series. This algorithm enables us to detect low period cycles using a very small set of data points. The influence of noise is investigated in some detail.
引用
收藏
页码:4733 / 4736
页数:4
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