DYNAMICAL SYSTEMS AND TESSELATIONS: DETECTING DETERMINISM IN DATA

被引:47
作者
Mees, Alistair I. [1 ]
机构
[1] Univ Western Australia, Dept Math, Nedlands, WA 6009, Australia
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1991年 / 1卷 / 04期
关键词
D O I
10.1142/S0218127491000579
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Data measurements from a dynamical system may be used to build triangulations and tesselations which can at least when the system has relatively low-dimensional attractors or invariant manifolds give topological, geometric and dynamical information about the system. The data may consist of a time series, possibly reconstructed by embedding, or of several such series; transients can be put to good use. The topological information which can be found includes dimension and genus of a manifold containing the state space. Geometric information includes information about folds, branches and other chaos generators. Dynamical information is obtained by using the tesselation to construct a map with stated smoothness properties and having the same dynamics as the data; the resulting dynamical model may be tested in the way that any scientific theory may be tested, by making falsifiable predictions.
引用
收藏
页码:777 / 794
页数:18
相关论文
共 35 条
[1]  
Aihara K., 1990, BIFURCATION PHENOMEN
[2]   SINGULAR-VALUE DECOMPOSITION AND THE GRASSBERGER-PROCACCIA ALGORITHM [J].
ALBANO, AM ;
MUENCH, J ;
SCHWARTZ, C ;
MEES, AI ;
RAPP, PE .
PHYSICAL REVIEW A, 1988, 38 (06) :3017-3026
[3]  
Albano AM, 1987, CHAOS BIOLOG SYST, P207, DOI 10.1007/978-1-4757-9631-5_24
[4]   3-DIMENSIONAL AND 4-DIMENSIONAL SURFACES [J].
BARNHILL, RE ;
LITTLE, FF .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1984, 14 (01) :77-102
[5]   COMPUTING DIRICHLET TESSELLATIONS [J].
BOWYER, A .
COMPUTER JOURNAL, 1981, 24 (02) :162-166
[6]   NONLINEAR PREDICTION OF CHAOTIC TIME-SERIES [J].
CASDAGLI, M .
PHYSICA D, 1989, 35 (03) :335-356
[7]  
Casdagli M., 1991, P NATO SANT FE I C N
[8]  
Crutchfield J. P., 1987, Complex Systems, V1, P417
[9]   ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS [J].
ECKMANN, JP ;
RUELLE, D .
REVIEWS OF MODERN PHYSICS, 1985, 57 (03) :617-656
[10]   PREDICTING CHAOTIC TIME-SERIES [J].
FARMER, JD ;
SIDOROWICH, JJ .
PHYSICAL REVIEW LETTERS, 1987, 59 (08) :845-848