On determining the dimension of chaotic flows |
| |
Authors: | Harold Froehling J.P. Crutchfield Doyne Farmer N.H. Packard Rob Shaw |
| |
Affiliation: | Physics Department, University of California, Santa Cruz, CA 95064, USA |
| |
Abstract: | We describe a method for determining the approximate fractal dimension of an attractor. Our technique fits linear subspaces of appropriate dimension to sets of points on the attractor. The deviation between points on the attractor and this local linear subspace is analyzed through standard multilinear regression techniques. We show how the local dimension of attractors underlying physical phenomena can be measured even when only a single time-varying quantity is available for analysis. These methods are applied to several dissipative dynamical systems. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |